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    à8Va9F  ã                   @   s¤  d dl mZmZmZmZmZmZmZmZm	Z	m
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DerivativeÚsymbolsÚcollectÚFunctionÚfactorÚWildÚSÚcollect_constÚlogÚfractionÚIÚcosÚAddÚOÚsinÚrcollectÚMulÚPowÚradsimpÚdiffÚrootÚSymbolÚRationalÚexpÚAbs)Ú	unchanged)Ú_unevaluated_Mul)Ú_unevaluated_AddÚcollect_sqrtÚfraction_expandÚcollect_abs)Úraises)ÚxÚyÚzÚaÚbÚcÚdc            
      C   s2  t dƒ} t dƒ}t dƒ}t dƒ}ttd|  ƒƒt dƒdfks J ‚tdd|   ƒdt dƒ ks0J ‚td| |  ƒt dƒ t dƒ ksCJ ‚ttdd|  |  ƒƒt dƒ t dƒ d dfks^J ‚ttd| | |  ƒƒt d	ƒ dt dƒ  dt dƒ  d
fksJ ‚ttdd|  | |  ƒƒdt dƒ dt dƒ  dt dƒ  dt dƒ  dt d	ƒ  d dt dƒ  dt dƒ  dfks½J ‚ttd| | | |  ƒƒdt dƒ dt dƒ  dt dƒ  dt dƒ  dt dƒ  dt dƒ  dt d	ƒ  d t dƒ  d!fksÿJ ‚tdd| d  |d  | |  ƒ}td"| jƒd#ksJ ‚td| ƒd| ks*J ‚td| d$d% ¡ d| d  |d  | | ksEJ ‚td| d  ƒt dƒd ksVJ ‚td| t | | |  ƒd&t dƒ td  d&t dƒ td   d&t dƒ td   d&t dƒ td   d't dƒ td   d&t d	ƒ td   d&t dƒ td   d&t dƒ td   d(t dƒ td   d)t dƒ td   d*t dƒ td   d+t dƒ td   d,t dƒ td   d-t dƒ td   d&t d	ƒ td   d.t dƒ td   d/t dƒ td   d0t dƒ td   d1t dƒ td   d2t dƒ td   d3t dƒ t  dt d	ƒ t  d4t dƒ t  d5t dƒ t  d6t dƒ  d7t dƒ  d8t dƒ  d9t dƒ  d#td&  d:td   d;td   d<td   d=  ksJ ‚td| t | t  | |  ƒt dƒt tt d  dt dƒ t  t dƒt  t dƒt tt d   dt dƒ t  t dƒt  t dƒtt d   t dƒtt d   dt dƒ  dt dƒ  dtd  d&td  t  d
td  td   d$td   d&t td   d-t t  dtd   d$td   d&  ks"J ‚td| t | t  | t  | t	   ƒt dƒdt dt  dt  dt	   ksMJ ‚tdd| t  | t  | t  | t	   ƒt dƒt t dƒt  t dƒt  t dƒt	  d dtd  dt t  dt t  dt t	  dtd   dt t  dt t	  dtd   dt t	  dt	d   d  ks¾J ‚tt
d t t
t tƒ  ƒt tƒt
 ksÕJ ‚tt
d t  t
t tƒ  ƒt tƒt
  ksîJ ‚tddt tt   ƒt t d t td dt  d  ksJ ‚tdt t
 tt t
ƒ   ƒt t t
ƒ tt
 td t
   ks3J ‚ddt dƒ  t dt dt t
ƒ   }t|ƒtddt dƒ   dt dt t
ƒ   ksbJ ‚td| ƒd>t d?t dƒ t  d?t t
ƒ  d?t dƒ t t
ƒ  d?t d?td  d?t
    ks•J ‚tdddt dƒ   ƒttjdt dƒ d@dAd ks²J ‚tdBd@dC}ttd t dƒtd   t dƒt |  ƒtd t dƒtd   t dƒt |  ksåJ ‚tdt ddt dƒ  ƒ ƒt dƒ t dƒ ksÿJ ‚tdt ddt dƒ  ƒd  ƒt dƒ t dƒ d  ksJ ‚ttdt tƒ ƒƒt tƒtfks1J ‚ttdt dt d ƒ ƒƒt dt d ƒdt d fksPJ ‚ttdt dtd  ƒ ƒƒt dt d ƒdt d fksoJ ‚tdDƒ}t|ƒ ¡ dEdtddƒ  ddtddƒ   d dt dƒ  ks–J ‚tdt dƒ d tj t dƒ d tj d   ƒdksµJ ‚dFt dƒ t t dƒd ƒ t d&t dƒ d- ƒ dGt dƒ t dHt dƒ d- ƒ t t dƒ d ƒ  d2t dƒ t dHt dƒ d- ƒ t t dƒ d ƒ  d2t dƒ t t dƒ d ƒ t d&t dƒ d- ƒ  d2t dƒ t dHt dƒ d- ƒ t t dƒd ƒ  d2t dƒ t t dƒ d ƒ t d&t dƒ d- ƒ  d2t dƒ t dHt dƒ d- ƒ t t dƒd ƒ  dIdJt dƒ  d
t dƒ t t dƒd ƒ d(t dƒ t t dƒ d ƒ  d   }t|ƒtju s’J ‚dt t dƒd dt dƒ  dt dƒ  dt dƒ  ƒ d }t|ƒt t dƒdt dƒ  dKt dƒ  dLt dƒ  ƒ dMt dLƒ dNt dOƒ  dPt dƒ  dQt dƒ  dRt dƒ  dS dTt dƒ  dUt dKƒ   dV d ks J ‚t dƒt dƒ }td|d  ƒt dƒt dƒ d ksJ ‚td| d  ƒt dƒt dƒ d  ks4J ‚td| t  ƒ| t  ksFJ ‚td|t  ƒt dƒt dƒ t ks[J ‚ttddt dƒ  t ƒƒddt  dt dƒ dt   ks|J ‚tddt dƒ  ƒ}t|ƒtt dƒ d ƒks–J ‚t|d ƒtt dƒ d ƒd ksªJ ‚td| ƒdtt dƒ d ƒ ks¾J ‚td| ƒdtt dƒ d ƒ ksÒJ ‚tt|t tƒ ƒƒt tƒtt dƒ d ƒ tfksîJ ‚dt dƒ }	tt|	 d@dWt t dƒ d  ks	J ‚ttt
|	  d@dWtt
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ƒ }t|ƒtt tƒt t
ƒdt
 ƒks\J ‚t|d@dW|ksgJ ‚tt tƒt t
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   é   é   é7   é=   é   é]   é.   é5   éG   iÎÿÿÿé*   é…   é"   éF   é‘   é   éi   é¹   é>   é‡   é×   l   NÝ”>ˆAé   é   )Z	max_termsé   é´   é   éT   éd   ét   éH   é(   i  iÎ  i.  éþ   éx   i  éR   éb   év   é;   i'  i  ià  i8  iØ  i™  i÷ÿÿÿé	   F©ZevaluateÚA©ZcommutativezE-(2 + 2*sqrt(2) + 4*2**(1/4))/(1 + 2**(3/4) + 3*2**(1/4) + 3*sqrt(2))éþÿÿÿiÿÿÿih  iøÿÿÿi`sÿÿi   é   é#   i)NÿiÜ éÒ   iæ i´ iôò iÅW ivs iW„~ iâ‚M)Zsymbolic)r   r   r   ÚlenÚargsÚexpandr&   r'   r(   r)   r$   r#   r   r   r	   ÚHalfr   r   ZNaNr   r   Úumul)
Zr2Zr3Zr5Zr7r%   Úer[   ÚeqÚbaseÚr© rj   úC/usr/lib/python3/dist-packages/sympy/simplify/tests/test_radsimp.pyÚtest_radsimp   s"   
ÿÿÿ$ÿ:ÿ
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ÿ*.$*B (((8*."
ÿ&>rl   c                  C   sŠ   t ddd\} }t| d |d  ƒ}| t|  | | t|  |  }t|ƒt | t|  t| d |d  ƒ d  d|  |  ksCJ ‚d S )Nzc pT©Zpositiver*   )r   r   r   r   )r(   ÚpÚsr'   rj   rj   rk   Útest_radsimp_issue_3214™   s    Frp   c                  C   sü  t dƒ\} }}}td| ƒdksJ ‚t| ||   | ƒ| d|  ks"J ‚t| | d  | ƒ| | d  ks3J ‚t| d || d   | ƒ| d d|  ksJJ ‚t| d ||   | ƒ| | | d  ks_J ‚td| d  || d   d|  |  | gƒ| d d|  d|  |  ks…J ‚td| d  || d   d|  |  |gƒd| d  || d d|     ks­J ‚td| |  d  ¡ | ƒd| d  ¡ | dd| d   ¡   | d dd| d   ¡   | d dd|   ¡   | d  ksîJ ‚| | }t||jƒ|ksüJ ‚dS )z Collect with respect to a Symbolúx,y,z,nr.   r*   r+   r1   r0   N)r   r   rc   Zfree_symbols)r#   r$   r%   ÚnÚexprrj   rj   rk   Útest_collect_1    s&   "".*LP&ÿÿþ
þrt   c                  C   sh   t dƒ\} }}t| t|ƒt|ƒ  |t|ƒt|ƒ   t|ƒt|ƒ ƒ| | t|ƒt|ƒ  ks2J ‚dS )zCollect with respect to a sumza,b,xN)r   r   r   r   )r&   r'   r#   rj   rj   rk   Útest_collect_2³   s   (ÿÿru   c                  C   s  t dƒ\} }}tdƒ}t dƒ\}}}}t| d ||  | ƒ||tddƒ  ks+J ‚td||d   || ƒd||d   ksBJ ‚t|| | | |  || ƒ|| d|   ks[J ‚td||  | | |  || ƒd|| d|    ksxJ ‚t| | ||ƒ ||||ƒ   |||ƒ ƒ|| |  ||ƒ ks›J ‚t| | t|ƒ ||t|ƒ   |t|ƒ ƒ|| |  t|ƒ ks¾J ‚t| |d  t|ƒd  ||t|ƒ d   |t|ƒ ƒ|d t|ƒd  | |  ksëJ ‚t|| | | | | |  || | ƒd|  | | | ksJ ‚dS )z!Collect with respect to a productza,b,cÚfrq   rK   r.   r*   N)r   r   r   r   r   )r&   r'   r(   rv   r#   r$   r%   rr   rj   rj   rk   Útest_collect_3º   s   0.2:FF8ÿHrw   c                  C   sŒ   t dƒ\} }}}t| ||  |||   || ƒ|| | |  ks#J ‚t| |d|   ||d|    || ƒ|d|  | |  ksDJ ‚dS )zCollect with respect to a powerza,b,c,xr*   N©r   r   )r&   r'   r(   r#   rj   rj   rk   Útest_collect_4Ï   s   6Fry   c                  C   sþ   t dƒ\} }}}}t|d |d  |||d  d   | | |  ||d  |gƒ|d|  |d |d    |d |d   |d|   |d |d  d|   fv sTJ ‚td||  || d   ¡ ||gƒd| |dd|    |d  |d  ks}J ‚dS )zCollect with respect to a tuplez	a,x,y,z,nr*   r1   r.   N)r   r   rc   )r&   r#   r$   r%   rr   rj   rj   rk   Útest_collect_5Ø   s   @*"
þÿ&ÿrz   c                  C   sF   t dƒ} t| d | d d  | d dd| d  | d d ks!J ‚dS )z-Unevaluated collect with respect to a productr&   r*   r.   FrZ   Nrx   )r&   rj   rj   rk   Útest_collect_pr19431â   s   >r{   c                  C   sÈ  t } tdƒ}tdƒ\}}}| ||ƒ|ƒ}| ||ƒ||ƒ}t|| ||  |ƒ|| | ks/J ‚t|| ||ƒ || ||ƒ  |ƒ|| | ||ƒ ksKJ ‚t|| ||  |ƒ|| | ||ƒ ksaJ ‚td||ƒ d|  |ƒd||ƒ d|  kszJ ‚t||ƒ||ƒt||ƒ|ƒ  |t||ƒ|ƒ ||ƒ  ||ƒ |¡ƒ|||ƒ ||ƒ | ||ƒ|ƒ ||ƒ ksµJ ‚t||ƒ||ƒt||ƒ|ƒ  |t||ƒ|ƒ ||ƒ  ||ƒ |¡dd|||ƒ ||ƒ | ||ƒ|ƒ ||ƒ ksòJ ‚td||ƒ d||ƒ t||ƒ|ƒ  |t||ƒ|ƒ ||ƒ  ||ƒ |¡ddd||ƒ |||ƒ  | ||ƒ|ƒ d||ƒ  ks8J ‚d||  | ||ƒ }t| ¡ |ƒ||||ƒ d||ƒ   d||ƒ  ksbJ ‚d S )Nrv   úx,a,br,   r+   T©Úexactr.   )r   r   r   r   r   rc   )ÚDrv   r#   r&   r'   ÚfxÚfxxrf   rj   rj   rk   Útest_collect_Dè   s(   &8,2F(ÿJ(ÿR0
ÿ@r‚   c               
   C   s†  t t d d  ¡ } t| t ƒtd dtd   dt  t d  t d dt d   t dtd  dt  d   d ks=J ‚t| t tƒt d dt d  td   dt  td d   td d  kscJ ‚t| t ddtjtd dtd   dt  d t dtd  dt  d t d dt d t d diks—J ‚t| t tddtjtd d t dtd d  t d ttdƒtd ƒt d diksÁJ ‚d S )Nr.   r+   r*   r0   FrZ   )r#   r&   rc   r   r   r	   ÚOnere   )rv   rj   rj   rk   Útest_collect_funcþ   s$   >ÿ
ÿ8

ÿ"(
ýþr„   c                  C   s  t dƒ\} }}}t|||  ||d   t|d ƒ |ƒ|d| |d  t|d ƒ  ks/J ‚t|||  |d  t|d ƒ |ƒ|d| t|d ƒ  |d  t|d ƒ ksZJ ‚| | ||  t|d   t|d   t|d ƒ }|| |  |d tt   t|d ƒ }t||ƒ|ks‘J ‚t||dd|ksœJ ‚t| | ƒ |dd¡}t|t| ƒt| ƒgƒt| ƒt|ƒ |dd¡ t| ƒt|ƒ |dd¡  ksÎJ ‚t|t| ƒt| ƒgddt| ƒt|ƒ |dd¡ ¡  t| ƒt|ƒ |dd¡ ¡   t|d ƒ ksJ ‚d S )	Nza,b,x,tr*   r+   r.   F)Zdistribute_order_termr   r4   )	r   r   r   r(   r)   r   Zseriesr   ZremoveO)r&   r'   r#   Útrv   Úgrj   rj   rk   Útest_collect_order  s(   N$*ÿ4(2ÿÿ
ÿÿr‡   c                   C   sˆ   t td t tt  t t tt  tƒttdt td    tt  ks'J ‚t ttd td   ƒtƒttd td   ƒksBJ ‚d S )Nr*   r.   )r   r#   r$   r   r%   rj   rj   rj   rk   Útest_rcollect'  s   (ÿ:rˆ   c                  C   sT   t } tdƒ}tdƒ\}}}| ||ƒ||ƒ}t|| ||  |ƒ|| | ks(J ‚d S )Nrv   r|   )r   r   r   r   )r   rv   r#   r&   r'   r   rj   rj   rk   Útest_collect_D_0-  s
   *r‰   c                  C   sX  t dƒ\} }}}tdƒ}tdƒ}tdƒ}t||ƒ| ||ƒ  ||ƒƒd|  ||ƒ ks-J ‚t|||ƒ| |||ƒ  ||ƒƒ|||ƒ| |||ƒ  ksLJ ‚t|||ƒ| |||ƒ  |||ƒƒd|  |||ƒ ksiJ ‚t|||ƒ| |||ƒ  |||ƒƒ|||ƒ| |||ƒ  ks‰J ‚t|||ƒ| |||ƒ  |||ƒƒd|  |||ƒ ks¦J ‚t| |d |  |d |  || ƒd|  |d |  ksÅJ ‚t| |d |  |d |  || ƒ| |d |  |d |  ksèJ ‚t| |d |  |d |  |d | ƒd|  |d |  ks
J ‚t| |d |  |d |  || ƒd|  |d |  ks*J ‚dS )z4Collect with respect to functions with Wild argumentza b x yrv   z.1z.2r.   N)r   r   r   r   )r&   r'   r#   r$   rv   Zw1Zw2rj   rj   rk   Útest_collect_Wild6  s"   2>:@:>$ÿ(
ÿDrŠ   c                  C   s|  t dtdƒ dt tdƒ  ƒddtdƒ t tdƒ  ks J ‚t dtdƒ dt tdƒ  tdƒƒdtdƒ dt tdƒ  ksCJ ‚t tdƒdtdƒ  tdƒ ttdƒ  ƒtdƒtd tdƒ  tdƒ kskJ ‚t dt dt  d dƒt dt dt  d ƒ  kr˜ttjtdtt ddddks›J ‚ J ‚t t t	 ƒtdtt	 ddks­J ‚t dt dt  dt	  dƒtdtt t	 ddksÉJ ‚t dt dt  dt	  d	ƒt
dt td	tt	 ddƒksèJ ‚td
dtdƒ  ƒt tdtdƒ ƒt  d } t| d ƒdttdƒd ƒ tdƒt t  d ksJ ‚t tt td  td  ƒtt ttjtt dd ks<J ‚d S )Nr*   r+   r1   r,   r.   FrZ   r/   r]   r6   )r
   r   r&   r#   r$   r   r	   rƒ   r   r%   r   r   r'   rd   ©rg   rj   rj   rk   Útest_collect_constI  s4   ÿ$ÿ*ÿÿþ$ÿÿ0
&
ÿBrŒ   c                  C   sD  t dƒ} | tƒ t¡}| tƒ| | tƒ|  }t|tdƒƒ| tƒ|d  | ks*J ‚| tƒ| tƒ|  t| | tƒ  }t||ƒt| tƒ | tƒ | | tƒ ksSJ ‚t|| tƒƒt| | d | tƒ kshJ ‚| tƒ| | tƒ|  }t|| tƒ|gƒ| tƒd|  | ks‰J ‚t||| tƒgƒ|d| tƒ  | tƒ ks J ‚d S )Nrv   Úwr.   )r   r#   r   r   r   )rv   r€   rf   rj   rj   rk   Útest_issue_13143e  s   &$.**2rŽ   c                   C   sˆ   t ttdt   ttdt    tt ƒtt tt d  ks!J ‚t tddt   tddt    dt ƒtt dt d  ksBJ ‚d S )Ng       @r*   )r   r&   r$   r#   r'   rj   rj   rj   rk   Útest_issue_6097s  s   BFr   c                  C   sh   t t t t  } | jddt| ƒ  kr!t t td  t  ks$J ‚ J ‚|  ¡ ttd t   ks2J ‚d S )NT)Zfracr*   )r#   r$   rc   r    r‹   rj   rj   rk   Útest_fraction_expandx  s   8 r   c               
   C   sB  t tdƒ\} }}tddd}ttjƒdksJ ‚t| ƒ| dfks!J ‚td|  ƒd| fks-J ‚t| | ƒ| |fks9J ‚t| d ƒ| dfksEJ ‚t| | | ƒ| | |fksUJ ‚t| ||  ƒ| || fkseJ ‚td|d  ƒd|d fksuJ ‚t| |d  ƒ| |d fks…J ‚t| d d | ƒ| d d |fks™J ‚t| |d  |d  ƒ| |d  |d fks±J ‚tt|  ƒd	d
t|  ƒdfksÃJ ‚td| |  d d	d
dtd| | ddfksÜJ ‚t| | | ƒ| | |fksìJ ‚t| |d  | ƒ| |d  |fksJ ‚tdd	d}tt|ƒƒdt| ƒfksJ ‚tt| ƒƒt| ƒdfks(J ‚tdd	d}tt| ƒt|ƒ d	d
t| ƒt|ƒ dfksIJ ‚tddtjdd}t|ƒdks[J ‚t|d	d
tdddddfksmJ ‚tddtjtjt	dddddd}t|ƒdks‡J ‚t|d	d
tddddtdddddfksŸJ ‚d S )NZxyzr[   Fr\   )r.   r*   r.   r*   r-   Tr}   rZ   r/   rr   )Únegativern   rm   )r.   r1   )
Úmapr   r   r	   rd   r   r   r   r   r   )r#   r$   r%   r[   rr   rn   Úmrj   rj   rk   Útest_fraction~  s<       (0$2 * "6$"
ÿr”   c                  C   sT   t dƒ\} }}}}|d | || d   |  ¡ }t|| d | |gƒ|ks(J ‚d S )NzaA Re a b Dr+   )r   rc   r   )ZaAZRer&   r'   r   rf   rj   rj   rk   Útest_issue_5615©  s    "r•   c                  C   s^   ddl m} m}m} | |dddƒjŽ jj}t||ƒ ¡ ƒdks!J ‚t|t	|ƒƒƒdks-J ‚d S )Nr   )ÚPolygonÚRegularPolygonÚdenom)r   r   r.   r,   gê-™—q=)
Úsympyr–   r—   r˜   ZverticesZcentroidr#   Úabsrr   r   )r–   r—   r˜   r#   rj   rj   rk   Útest_issue_5933¯  s   r›   c                     s´   t ddd\‰ ‰t dƒ\} }tt‡ ‡fdd„ƒ t| | || d   ˆ ƒ| | || d   ks1J ‚t| | || d   ˆ ˆ  ˆˆ   |ƒ|d|  d  ˆ ˆ  ˆˆ   ksXJ ‚d S )	Nza bFr\   zx yc                      s   t ˆ ˆ ˆˆ   ˆ ƒS )N)r   rj   ©r&   r'   rj   rk   Ú<lambda>¹  s    z"test_issue_14608.<locals>.<lambda>r.   r*   )r   r"   ÚAttributeErrorr   )r#   r$   rj   rœ   rk   Útest_issue_14608¶  s
   2RrŸ   c                  C   sÈ   t tƒt tƒ } t| ƒ| ksJ ‚ttt tƒt tƒƒsJ ‚ttt ƒ}t|tƒs)J ‚tt tƒt tƒ ƒ|ks7J ‚tdtt tƒt tƒ ƒ ƒdt|ƒ ksMJ ‚t	ddd}t|t d| ƒ ƒj
du sbJ ‚d S )Nr.   rn   Trm   )rš   r#   r$   r!   r   r   r   Ú
isinstancer   r   Zis_commutative)ro   Zansrn   rj   rj   rk   Útest_collect_abs¾  s   ,"r¡   c                  C   s*   t dt d ƒ} t| t tƒƒ| ksJ ‚d S )Nr+   r1   )r   r#   r   r‹   rj   rj   rk   Útest_issue_19149Ì  s   r¢   c                  C   sr   t dƒ\} }| d |d  dd|  |   }t|| d d|  fdd}|| d |d d|  dd|  iks7J ‚d S )Nza, br*   r.   r-   FrZ   rx   )r&   r'   rs   Z	collectedrj   rj   rk   Útest_issue_19719Ð  s    ,r£   c                   C   sd   t dtttd ƒ  ƒdtttd ƒ  ksJ ‚t dtttd ƒ  ƒdtttd ƒ  ks0J ‚d S )Nr.   r*   )r   r#   r   rj   rj   rj   rk   Útest_issue_21355Ø  s   04r¤   N)Ir™   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   Zsympy.core.exprr   Zsympy.core.mulr   re   Zsympy.simplify.radsimpr   r   r    r!   Zsympy.testing.pytestr"   Z	sympy.abcr#   r$   r%   r&   r'   r(   r)   rl   rp   rt   ru   rw   ry   rz   r{   r‚   r„   r‡   rˆ   r‰   rŠ   rŒ   rŽ   r   r   r”   r•   r›   rŸ   r¡   r¢   r£   r¤   rj   rj   rj   rk   Ú<module>   sB   p $ 	
	+