a
    khh                  
   @   s|  d 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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mZmZ dd
l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% ddl&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0 ddl1m2Z2 ddl3m4Z4m5Z5 ddl6m7Z7 ddl8m9Z9m:Z: ddl;m<Z< ddl=Z=ddl>m?Z? e
d\
Z@ZAZBZCZDZEZFZGZHZIdd ZJdd ZKdd ZLdd ZMdd  ZNd!d" ZOd#d$ ZPd%d& ZQd'd( ZRd)d* ZSd+d, ZTd-d. ZUd/d0 ZVd1d2 ZWd3d4 ZXd5d6 ZYd7d8 ZZd9d: Z[d;d< Z\d=d> Z]d?d@ Z^dAdB Z_dCdD Z`dEdF ZadGdH ZbdIdJ Zce:dKdL ZddMdN ZedOdP ZfdQdR ZgdSdT ZhdUdV ZidWdX ZjdS )YzBTests for algorithms for computing symbolic roots of polynomials.     )IRationalpi)S)SymbolWildsymbols)	conjugateimre)exp)rootsqrt)	Piecewise)acoscossin)ZZInterval)powsimp)Polycyclotomic_poly	intervalsnrootsrootof)
root_factorsroots_linearroots_quadraticroots_cubicroots_quarticroots_quinticroots_cyclotomicroots_binomialpreprocess_rootsroots)legendre_poly)PolynomialErrorUnsolvableFactorError)_nsort)raisesslow)verify_numericallyN)productza,b,c,d,e,q,t,x,y,zc                 C   s   t dd | D }t| d | t| d | ks6J t|t| dD ]6}| |d  | | ksF| |d  t| | ksF dS qFdS )Nc                 s   s   | ]}|j rd ndV  qdS )   r   Nis_real.0i r4   N/var/www/auris/lib/python3.9/site-packages/sympy/polys/tests/test_polyroots.py	<genexpr>(       z_check.<locals>.<genexpr>   r.   FT)sumsortedlistrangelenr	   )r%   Znrealixr4   r4   r5   _check$   s    $r?   c                   C   s*   t tdt d ttddgks&J d S )Nr8   r.   )r   r   xr   r4   r4   r4   r5   test_roots_linear2   s    rB   c                  C   s  t tdtd  tddgks"J t tdtd  dt  ttdddgksRJ t tdtd  d tt td d ttd d gksJ t tdtd  dt  d tdttd d  dttd d  gksJ ttdtd  dt  d t  td dt t	 dt
 t	  tt
  t  tt tt	d   t
t	d   tt
   } t t| tt	 tt
  tt
  ttt t
t  tt  tt
  dt t
 t	d   tt
   t	 tt
  tt
  ttt t
t  tt  tt
  dt t
 t	d   tt
   gksJ tttd  dt  dt  t} t | tdtd  d  t dt  tdtd  d t dt  gksJ ttd td  d t  td  d t} t | dtd d gksJ ttdtd  d t} t | }|t|ks
J td	td  d
t  d } dd | jddD dd | jddD ksXJ tdddD ]B\}}}t|td  |t  | } t | }|t|ksdJ qdd S )Nr8   r            r@   r.   i   i  c                 S   s   g | ]}| d qS r8   nr2   wr4   r4   r5   
<listcomp>P   r7   z(test_roots_quadratic.<locals>.<listcomp>T)Zradicalsc                 S   s   g | ]}| d qS rH   rI   rK   r4   r4   r5   rM   Q   r7   F)r8   )r   r@   )r   r   rA   r   r   r   r?   	all_rootsaecdbyr)   r-   )frZ_a_bZ_cr%   r4   r4   r5   test_roots_quadratic6   s<    "0@N&TTT
"@
,

rY   c                  C   s   t td t td  t t} t| ttd tdt d  dttd t d td  dttd tdt d   dttd t d td   diksJ d S )NrF   r8      r.   )r   rA   r   r%   r   eqr4   r4   r5   test_issue_7724X   s     r]   c                     s   t dtddgt  tt  tt} tddtd d  fdd| D }t|ttt  ttkstJ t	 fdd	|D sJ d S )
Nr.   rN   rD   r8      c                    s   g | ]}| t qS r4   )subsrU   r2   rW   )zr4   r5   rM   e   r7   z#test_issue_8438.<locals>.<listcomp>c                 3   s.   | ]&}  tt|ijd dddkV  qdS )r8   TZchopr   N)r_   rU   rA   rJ   r1   pra   r4   r5   r6   i   r7   z"test_issue_8438.<locals>.<genexpr>)
r   rU   rA   Zas_exprr   r   r   setr_   all)r%   postr4   rc   r5   test_issue_8438a   s    rh   c                     s   t dtd  d tt td d   } t| s6J t td dtd   d t  fddtdD }t td dtd   d t } | |ksJ t| sJ t dtd  d  } t| sJ tt dtd	  d  d	ksJ d S )
NrF      r.   r8   rZ   rE   c                    s   g | ]}t  |qS r4   r   r1   rV   r4   r5   rM   p   r7   z#test_issue_8285.<locals>.<listcomp>
   )r   rA   rO   r?   r<   r=   )r%   ror4   rk   r5   test_issue_8285l   s    *"rn   c                  C   s   t td d t td d   } t| s0J t td dtd   d t } t| s^J t td t d  } t| sJ t td dtd   d t } t| sJ d S )Nr8   rF   rE   rC   r.   )r   rA   rO   r?   r%   r4   r4   r5   test_issue_8289{   s    $""rp   c                     s   t td d d td d d  td   ddt dt dtdt  dtdt  gksbJ td dtd   d   fddtdD } t   | ksJ t|  d S )Nr.   r8   rF   rl   c                    s   g | ]}t  |qS r4   rj   r1   rd   r4   r5   rM      r7   z$test_issue_14291.<locals>.<listcomp>)r   rA   rO   r   r   r<   r?   )ansr4   rq   r5   test_issue_14291   s    .,rs   c                  C   s>   t td ttt  t tdd} t| }t|dks:J d S )NrC   EXdomain)r   rU   r   rA   r%   r=   )r\   Zroots_dr4   r4   r5   test_issue_13340   s    "rw   c                     sx   t td td ddt    td ddt    tdd	t    d
 dt  t t } t fdd| D stJ d S )NrF   rC          r8   ii  ii  i
  i  c                 3   s   | ]} |d kV  qdS r   Nr4   r`   r[   r4   r5   r6      r7   z#test_issue_14522.<locals>.<genexpr>)r   rA   r   r%   rf   )roots_eqr4   r[   r5   test_issue_14522   s    Rr|   c                  C   s@   t ttd dtd   tt  d t} | d ts<J d S )NrF   rE   r8   rC   r   )r    r   trA   Zhas)solr4   r4   r5   test_issue_15076   s    *r   c                  C   sb   t td dtd td   dtd   dtd td   dt  t} t| }d|v s^J d S )NrF   ri   r8   rC   @   i   r   )r   rA   r   r%   )r\   r{   r4   r4   r5   test_issue_16589   s    Jr   c               	   C   sl  t tdtd  tg dks"J t ttd dtd   dt  d tg dksXJ ttd} t ttd t t| | tj tdt d   | tj tdt d   gksJ t ttd d tdtjttd d  tjttd d  gksJ t tdtd  dtd   dt  d td tjdt	dd d  dt	dd d  ks`J td  dtd   dt  d }t
|ddd	t t|tdd
  krbt	dddtd ttdtd d d  d  dtd ttdtd d  d td   d t	dd dtd ttdtd d  d td   d t	dd gkshn J d S )Nr8   rC   )r   r   r   r.   r.   r.   r.   r@   r   T)trigmultiple)r      ri      rN   rE   )r   r   rA   r   rU   r   Halfr   r   r   r%   r   r   r   r   )rW   r\   r4   r4   r5   test_roots_cubic   s,    "6

,0(
"
4>>r   c                     sd  t ttd tg dksJ t ttd td  tg dg dg dg dfv sXJ t ttd td  tg dg d	g d
g dfv sJ t ttd t t} tjttd d  tjttd d  tjtj g}t	| t
dt	|t
dksJ tg dD ]\}\}}}}|dkrD| |d td |td   }n<|dkr|||d tdd |td   |td   }td |td   |td   |t  |  t t t}t fdd|D sJ qttt td  td  td  dtd   tdd t t  }t fdd|D s:J tdddtd dtd   dtd   td   d  t t t}	t fdd|	D sJ tttd  td  t  t t  }tdd |D sJ tddtdddtddtdddtddddf}
|
D ]<t t t}tfd dt||D s"J q"d S )!NrF   r   r   r   r   rC   )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.   r8   key))r.   r8   rC   r   )rC   i	   r.   r8   rC   rF   r   )r   rD   rC   )rD   rZ   r   )rE   irD   ri      rx   c                 3   s&   | ]}  t|jd ddkV  qdS )Trb   r   Nr_   rA   rJ   )r2   Zair[   r4   r5   r6      r7   z%test_roots_quartic.<locals>.<genexpr>r.   c                 3   s    | ]}t  t|d V  qdS rz   r,   r_   rA   r1   r[   r4   r5   r6      r7   ra   T)negative   rZ   c                 3   s*   | ]"}t  t|fd ffdV  qdS )r@   r   Nr   r1   )r\   ra   r4   r5   r6      r7   c                 s   s   | ]}t |tkV  qd S N)typer   r1   r4   r4   r5   r6      r7   r@   )rU   ra   rN   c                 3   s&   | ]\}}t | | d V  qdS rz   )r,   r_   )r2   rL   s)repr4   r5   r6      r7   )r    r   rA   r   r   r   r   ZeroOner:   hash	enumerater   rf   qr   rU   r_   zip)lhsrhsr3   rP   rT   rR   rS   rr   r~   ZzansZrepsr4   )r\   r   ra   r5   test_roots_quartic   sR    

6
$
2, <0"r   c                	   C   sX   t dd tttd td ddt    dt dt   d dt  tD rTJ d S )	Nc                 s   s   | ]}t |tV  qd S r   )
isinstancer   r1   r4   r4   r5   r6      r7   z#test_issue_21287.<locals>.<genexpr>rF   r8   rC   rZ   r@   r.   )anyr    r   rA   r   r4   r4   r4   r5   test_issue_21287   s    
<r   c                     s   t d d t d d d dt d d   d t d dt d   dt d   dt   d	 f} | D ]: tt }t|dks~J t fd
d|D s^J q^d S )NrZ   r8   r.      n   rC   7   i	  i  c                 3   s,   | ]$}  t|d jdddkV  qdS )rl   gh㈵>rb   r   Nr   r`   r[   r4   r5   r6     r7   z%test_roots_quintic.<locals>.<genexpr>)rA   r!   r   r=   rf   )Zeqsr%   r4   r[   r5   test_roots_quintic   s    
"*r   c                   C   s  t tdtdddgksJ t tdtdddgks8J t tdtddtddttd d  tddttd d  gksJ t tdtddt tgksJ t tdtddtjttd d  tjttd d  gksJ t td	tddtt	d	  tt
t	d	   tt	d	  tt
t	d	   tt	tdd	  tt
t	tdd	   tt	tdd	  tt
t	tdd	   tt	tdd	 tt
t	tdd	   tt	tdd	 tt
t	tdd	   gksJ t td
tddtd d ttd d  td d ttd d  tdd ttd d  tdd ttd d  gks\J t tdtddtd d td  td d td  tdd td  tdd td  gksJ t tdtdddddgksJ t tdtdddddgksJ t tdtddddtdd dtdd gks>J t tdtddddt tgksdJ t tdtddddtdd tddd  tddd dtddd  tdd tddd  gksJ t tdtdddddtdd tddgksJ d S )Nr.   TZpolysr8   r@   rC   rF   rE   r^   ri   r   )ZfactorrZ   )r"   r   rA   r   r   r   r   r   r   r   r   r   r4   r4   r4   r5   test_roots_cyclotomic  sn    2 *((&&	



N
r   c               	   C   sH  t tdt tdgksJ t tdtd  tg dks>J t tdt d ttddgksdJ dtdd d } t tdtd  d t|  | t  |  | t  | | t  | | t  gksJ tt ttd	 d  td
dd}tddd}tt|td  | t}t t|td  | t}t|d t|d ksFJ t|d t|d ksdJ t	ddddD ]X\}}}}||kr|dkrqrt|t|  ||  }	t |	}
|
t
|
ksrJ qrttdtd  dtd   tdt tddtdt d   ddt ddt tddtdt d   diksDJ d S )NrZ   r   rF   r   r8   rN   rl   rC   ri   a1T)Znonnegativeb1r.   )r.   r8   )r@   r.   )r8   rC   rF   rZ   rx   r@   )r#   r   rA   r   r   r?   r   r   r   r-   r)   r%   rU   r   )Ar   r   Zr0r1rP   rT   r   rJ   rd   rr   r4   r4   r5   test_roots_binomial7  s2    "&. ""r   c                  C   sl  t t td  t t } tt| t\}}|dks6J |tt t td  t t tks\J td td  td td   tt  t  } tt| t\}}|dt ksJ |ttd td  t t  tksJ td td  td td   t  } tt| t\}}|dt ksJ |ttd td  t  tks<J td td  tt  t  } tt| t\}}|dt ks|J |ttd t t  tksJ td td  t  } tt| t\}}|dt ksJ |ttd t  tksJ td\}}}}d|d  |d  |d  d| t |d	  |d	  |d
   d|d  |d  |d  td  |d   d|d  |d  |d  td  |d   d|d  |d  |d  td  |d   d|d  |d  |d  td  |d   d|d  |d  |d  td  d|d    d| | |d	  td	  d|d    d|d  td  d  } tt| t\}}|d| | ||d   ksJ |dtd  dtd	   dtd   dtd   dtd   dtd   dtd   dt  d  ksJ ttd  td tt  tt	tttf d!} ttd  tt tt	tt d!}t| t|fkshJ d S )"Nr8   r.   rC   E,F,J,L [r|)s2^ ri   rx       83ll8r^         ]$=,y rE   r      /@:rZ   rl      D!^ rF   q 
    P   y   q    id i B i߰l   ul   /1g&l   g l   FW&k ru   )
rP   rU   rA   rT   r$   r   rR   r   r   r   )rV   ZcoeffZpolyEFJLgr4   r4   r5   test_roots_preprocessingX  sh    &,&$$ "****.&
"<

0$r   c                  C   s  t dti ksJ t tttjdiks*J t td ttjdiksFJ t td td  td   ttd dtddtddiksJ t dt d ttdddiksJ t dt d d ttdddiksJ t dt d d ttdddiksJ t dt d d ttdddiks(J t td d ttdtjdtj dt diks\J t td d d ttdtjdtj dt diksJ t dt d d  ttdddiksJ t dt d d  ttd	ddiksJ t dt d d  ttdddiksJ t dt d d  ttd	ddiksLJ t dt d d  ttdddikszJ t dt d d  ttd	ddiksJ t tt t	 d  tt	t diksJ t tt t	 d  tt	 t diksJ t td t d t  t ttdtjdiks6J t td dtd   d ttjdtj
diksjJ t td
 dtd   dtd   td  ttjddtd dtjddtd diksJ t td d ttdd ttd d  dtdd ttd d  dtd d ttd d  dtd d ttd d  dtjdtj dtdt diksnJ dtd  dtd   dtd   dtd   dtd
   dtd   dtd   dtd   } t | tjdtd dtddtdddtd	ddtdddtdddiks J t tt	 t t tt	 t t  ttt	 t t tt	 t  dikslJ t td td  t d tddi ksJ t td td  td   tddtd dtddtddiksJ t td td  td  td   tddtd dtddtddtddiks<J t td dtd   dt  d ttd ddt ddt diksJ t td dtd   dt  d tdddt ddt dtd diksJ t td t td dtd   dt  d  ttjdtjdtd ddt ddt diks6J tjtdd }}dtd d | }d| d }|d }tdt d }|| }| | }t td td  t d tdd| | | d| | ||  | d| | ||  | diksJ td dt  d tdtd  dt  tdt d } dd dD \}	}
td}t | t|	|
tddt |    d|	|
tddt |    d|	|
tddt |    d|	|
tddt |    diksJ td td  td  t d } dd d D \}}}t | t| |d|   t||d|   |   d| |d|   t||d|   |   d| |d|   t||d|   |   d| |d|   t||d|   |   dik	sJ td dt td   ddt  dtd   t  t dtd   } t | ttjdtjtjt  tjtddt  td  dtd     dtjtjt  tjtddt  td  dtd     dik
sJ t tt	 t td  dtd   dt  d tddi k
sJ t tt	 t td  dtd   dt  d tddi ksJ t td d td!d"tjdtj diksBJ t td d td#d"tdt dikslJ t td td  ttjdtj diksJ t td td  td$d% d&tjdiksJ t td d td!dd'tj tjgksJ t td d td#dd'tt gksJ td(dd)\}}td || d  dt ||   d }t |td*d"d||  diksxJ t td tdd+tjtjtjgksJ t d,tdd+g ksJ td
 td  td  td  td  t d } t | t ttd  ttd  dt tttdd  tttdd  dt tttdd  tttdd  dtttd  ttd  dttttdd  tttdd  dttttdd  tttdd  diksJ td d | d   }t |t ttd  ttd  dt tttdd  tttdd  dt tttdd  tttdd  dtttd  ttd  dttttdd  tttdd  dttttdd  tttdd  dt dtdiksJ t td d-t  d }d.d |D d/ }d0d
td1  }|dt|d d d2t|d  ksNJ tddtd  td  d3dtd  td   td d t  d td4d5}t |dtd dddtd  dtd d diksJ td6td  d7td td   d8td   d0td td   d9td   d:td td   d;td   d<td td   d=td t  d=t  d> td4d5}t |td d dddtd  ddtd dd?dtd  dd	dtd  diksJ ttd dtd   d
td td   dtd t  d@t  dA dAtd  td4d5}t |dtd d ddtd d ddtd d diksxJ t tttd d d td4d5td tddtj tdt d    dtd tddtj tdt d    dtd tdd diksJ d S )BNr.   r   r8   rC   rF   r@   rZ   rl   rD   rE   ri   i i  i  i  i     r^   i  r   r   F)ZcubicsrN   T!      c                 S   s   g | ]}t | qS r4   r   r`   r4   r4   r5   rM     s   ztest_roots0.<locals>.<listcomp>))r   r   )r.   r   c                 S   s   g | ]}t | qS r4   r   r`   r4   r4   r5   rM     r7   ))r.   rF   )r.   ri   )rZ   ri   Zfilterr   c                 S   s   | j S r   )Zis_positive)rW   r4   r4   r5   <lambda>  r7   ztest_roots0.<locals>.<lambda>)	predicate)r   r   za, b)realRr   i  (   c                 S   s   g | ]}|j r|qS r4   r/   )r2   rxr4   r4   r5   rM   *  r7   r   l   i2  r   r   rt   ru   )            }   -            r      r   )r%   rA   r   r   expandr   r   r   rP   rT   ZNegativeOner   rR   rS   r   r_   ra   rU   r   r   r   r   r   r   )rV   Zr1_2Zr1_3Zx0x1Zx2Zx3Zx4Zx5Zr13_20Zr1_20s2Zr1_4Zr1_8Zr5_8arbrrd   r   rW   Z	real_rootZcrr\   r4   r4   r5   test_roots0  sX   D$((*48......,.44,&
:


(L,
,$
J(
0(

 <
 ****D::@@.*.
,(($(0**((	**((

*P<@

0 D
B ,,r   c                     s  t d\} }}}d | | |  | |  |  }d | |||  |    |  | | || |   | | ||   }tt| ddgksJ tt| ddgksJ t d\}}}}	}
}}|| ||  ||  |	| |
  |
 |	 | }|| | | |
||  |
  |	|	 ||   }tt|| | g dksTJ d dd   d  tt  }tdd	  fd
d|D D rJ dS )z6Just test that calculating these roots does not hang. z	a,b,c,d,xr8   r.   zzz,yy,xx,zy,zx,yx,kr   rC   ri   c                 s   s   | ]
}|V  qd S r   r4   r1   r4   r4   r5   r6   T  r7   z"test_roots_slow.<locals>.<genexpr>c                    s    g | ]}  |jd dqS )Trb   )r_   rJ   )r2   rirV   rA   r4   r5   rM   T  r7   z#test_roots_slow.<locals>.<listcomp>N)r   r;   r%   valueskeysr   )rP   rT   rR   rS   f1f2zzyyxxZzyZzxZyxke1e2r   r4   r   r5   test_roots_slow@  s    $H00$r   c                  C   s   t td t d tdd} t td t d tdd}t| |D ]\}}t|| dk s>J q>td dtd	 td
   ddtd  td   ddtd d   }t |dd} d}t| |D ]\}}t|| dk sJ qd S )Nr8   r.   Tr   g      ?g-q=rF   g      @g       @rC   g     S@g      8@g      b@g      "@)g؋~)g)cg3!	@g
 @绽|=)r%   rA   r   absr   )R1R2r   r2rV   r4   r4   r5   test_roots_inexactW  s    2r   c                  C   s  t d\} }}}d| d  |d  |d  d| t | d  |d  |d   d| d	  |d
  |d	  td
  |d   d| d  |d  |d  td  |d   d| d  |d  |d  td  |d   d| d  |d  |d  td  |d	   d| d
  |d	  |d
  td	  d|d    d|  | |d  td  d|d
    d|d  td  d  }t|ti ksJ t| tdd}g d}td}||  | ||d
   }t|t|ksJ t||D ]8\}	}
|	|}|d urt|| |
 dk sJ qd S )Nr   r   ri   rx   r   r^   r   r   rE   r8   r   r   rZ   rC   rl   r   rF   r   r   r   r   r   r   Tr   )g?|YcgOXLzGX@g'I^g@g|۰n@gdZw@g5`e@gS$Ȫ@gJm@rL   r   )	r   rA   r%   evalfr   r=   r   matchr   )r   r   r   r   rV   r   r   rL   rd   r   r   r   r4   r4   r5   test_roots_preprocessedi  s6    "****.&

r   c                   C   s   t td dt  d ddddiks(J t td dt  d ddddiksPJ t td dtd   td  dt  d ddddiksJ ttd	d
  d S )Nr8   r.   FstrictTrE   rZ   rC   c                   S   s0   t td dtd   td  dt  d ddS )NrE   r8   rZ   rC   Tr   )r%   rA   r4   r4   r4   r5   r     r7   z#test_roots_strict.<locals>.<lambda>)r%   rA   r*   r(   r4   r4   r4   r5   test_roots_strict  s    ((<r   c            	      C   s   ddt   dt d   dt d   dt d   } t| d	d
\}}t| }t| d	d}dd |D }dd |D }|| }dd |D }t|dd d}t|dd d}||fD ]D}t||D ]4\}}|jr||v sJ qt|t|f|v sJ qqd S )Nipi  i  r8   i
  rC   1   rF   T)rf   r   c                 S   s   g | ]\\}}}t ||qS r4   r   r2   rP   rT   _r4   r4   r5   rM     r7   z$test_roots_mixed.<locals>.<listcomp>c                 S   s8   g | ]0\\}}}t t|t|t t|t| qS r4   )r   r   r
   r   r4   r4   r5   rM     s   c                 S   s   g | ]}|  qS r4   )r   r`   r4   r4   r5   rM     r7   c                 S   s   |   S r   sort_keyrA   r4   r4   r5   r     r7   z"test_roots_mixed.<locals>.<lambda>r   c                 S   s   |   S r   r  r  r4   r4   r5   r     r7   )	rA   r   r   r%   r:   r   r0   r   r
   )	rV   _reZ_imZ_nrootsZ_srootsZ
_intervalsZ_rootsr3   rW   r4   r4   r5   test_roots_mixed  s"    0r  c                
   C   s  t tdttdtgksJ t ttttttgks<J t td d ttd td gksbJ t td t tttt ttt gksJ t td d d td td td td tt tt tt tt gksJ t ttd d tddttd tttd tttd d tgks(J t dtd  dtd   dtd   td  td	dtttd dtd   dtd   d gksJ d S )
Nr.   r8   rF   r   r   ri   r   rE   Q)r   r   rA   rU   r   r   r4   r4   r4   r5   test_root_factors  s    &.2*
4(r  c                     sR   d} t | tdd ttjj fdd  jdd}dd	 |D g d
ksNJ d S )Nr   Tr   c                      s    j dddS )NrC   rZ   )rJ   Zmaxsteps)r   r4   rq   r4   r5   r     r7   ztest_nroots1.<locals>.<lambda>rC   rI   c                 S   s   g | ]}t |qS r4   strr`   r4   r4   r5   rM     r7   z test_nroots1.<locals>.<listcomp>)@z-0.999z-0.996z-0.991z-0.983z-0.973z-0.961z-0.946z-0.930z-0.911z-0.889z-0.866z-0.841z-0.813z-0.784z-0.753z-0.720z-0.685z-0.649z-0.611z-0.572z-0.531z-0.489z-0.446z-0.402z-0.357z-0.311z-0.265z-0.217z-0.170z-0.121z-0.0730z-0.0243z0.0243z0.0730z0.121z0.170z0.217z0.265z0.311z0.357z0.402z0.446z0.489z0.531z0.572z0.611z0.649z0.685z0.720z0.753z0.784z0.813z0.841z0.866z0.889z0.911z0.930z0.946z0.961z0.973z0.983z0.991z0.996z0.999)r&   rA   r*   mpmathmpZNoConvergencer   )rJ   r%   r4   rq   r5   test_nroots1  s    r  c                  C   sj   t td dt  d t} | jdd}dd |D g dks@J | jdd}dd |D g d	ksfJ d S )
NrZ   rC   r.   rI   c                 S   s   g | ]}t |qS r4   r  r`   r4   r4   r5   rM     r7   z test_nroots2.<locals>.<listcomp>)z-0.332z-0.839 - 0.944*Iz-0.839 + 0.944*Iz1.01 - 0.937*Iz1.01 + 0.937*Ic                 S   s   g | ]}t |qS r4   r  r`   r4   r4   r5   rM     r7   )z-0.33199z-0.83907 - 0.94385*Iz-0.83907 + 0.94385*Iz1.0051 - 0.93726*Iz1.0051 + 0.93726*I)r   rA   r   )rd   r%   r4   r4   r5   test_nroots2  s    r  c                   C   s>   t tttd td tt  t t tdddks:J d S )NrC   r8   T)Z	composite)r=   r%   r   rU   r   rA   r4   r4   r4   r5   test_roots_composite  s    r  c                      s.   t td t t d  tt fdd d S )NrC   r.   c                      s   t  S r   ro   r4   r[   r4   r5   r     r7   z"test_issue_19113.<locals>.<lambda>)r   rA   r*   r'   r4   r4   r[   r5   test_issue_19113  s    r  c                   C   s>   t ddddt  d  d dt  dgd	d
ddgks:J d S )Nr.   rD   r   rF   r8   ri   r   r   Tr   )r%   r   r4   r4   r4   r5   test_issue_17454  s    r  c                   C   sN   t td t dgksJ t td d t dtdd   gksJJ d S )Nl          l       rC   rF   r8   )r   rA   Z
real_rootsr   r4   r4   r4   r5   test_issue_20913  s    r  c               	   C   s   t dd} dt |  td d|    }ttttd  td d  t|d| dtdt   d d|dtdt   d diksJ d S )Nr.   rC   r@   rZ   r8   )r   rP   r%   r   rA   r   r   )rQ   rW   r4   r4   r5   test_issue_22768  s    
 r  )k__doc__Zsympy.core.numbersr   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   r   Z$sympy.functions.elementary.complexesr	   r
   r   Z&sympy.functions.elementary.exponentialr   Z(sympy.functions.elementary.miscellaneousr   r   Z$sympy.functions.elementary.piecewiser   Z(sympy.functions.elementary.trigonometricr   r   r   Zsympy.polys.domains.integerringr   Zsympy.sets.setsr   Zsympy.simplify.powsimpr   Zsympy.polysr   r   r   r   r   Zsympy.polys.polyrootsr   r   r   r   r    r!   r"   r#   r$   r%   Zsympy.polys.orthopolysr&   Zsympy.polys.polyerrorsr'   r(   Zsympy.polys.polyutilsr)   Zsympy.testing.pytestr*   r+   Zsympy.core.randomr,   r
  	itertoolsr-   rP   rT   rR   rS   rQ   r   r}   rA   rU   ra   r?   rB   rY   r]   rh   rn   rp   rs   rw   r|   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r  r4   r4   r4   r5   <module>   sp   0"		:
0!< -
