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    lº”hõ¤ ã                   @   sæ  d dl mZmZ d dlmZ d dlmZ d dlmZm	Z	m
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 d dlmZ d dlmZ d dlmZmZ d dlmZmZmZmZmZmZ d d	lmZmZmZmZ d d
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dd„ Zdd„ Zdd „ Zd!d"„ Zd#d$„ Zd%d&„ Zd'd(„ Zd)d*„ Zd+d,„ Zd-d.„ Zd/d0„ Zd1d2„ Zd3d4„ Zd5d6„ Zd7d8„ Zd9d:„ Zd;d<„ Zd=d>„ Zd?d@„ ZdAdB„ ZdCdD„ ZdEdF„ Z dGdH„ Z!dIdJ„ Z"dKdL„ Z#dMdN„ Z$dOdP„ Z%dQdR„ Z&dSdT„ Z'dUdV„ Z(dWS (Y  é    )ÚQÚask)ÚAdd)ÚTuple)Ú
DerivativeÚFunctionÚdiff)ÚMod)ÚMul)ÚGoldenRatioÚTribonacciConstant)ÚEÚFloatÚIÚRationalÚooÚpi)ÚEqÚGtÚLtÚNe)ÚS)ÚDummyÚSymbolÚWildÚsymbols)Úsympify)Úbinomial)ÚAbsÚargÚ	conjugateÚimÚre)ÚLambertWÚexpÚlog)ÚatanhÚcoshÚsinhÚtanh)Úfloor)ÚcbrtÚrootÚsqrt)Ú	Piecewise)ÚacosÚasinÚatanÚatan2ÚcosÚsecÚsinÚtan)ÚerfÚerfcÚerfcinvÚerfinv)ÚIntegral)ÚAndÚOr)ÚMatrix)ÚMatrixSymbolÚSparseMatrix)ÚPolyÚgroebner)Ússtr)Údenom)ÚnsolveÚsolveÚsolve_linear)Únfloat)Úsolve_linear_systemÚsolve_linear_system_LUÚsolve_undetermined_coeffs)Ú_filtered_gensÚ_solve_lambertÚ_lambert)
Ú_invertÚunradÚchecksolÚposifyÚ_ispowÚ	det_quickÚdet_permÚ	det_minorÚ_simple_densÚdenoms)Úcm©ÚCRootOf)ÚslowÚXFAILÚSKIPÚraises)Úverify_numerically)ÚaÚbÚcÚdÚeÚkÚhÚpÚxÚyÚzÚtÚqÚmÚRé   c                 K   s   t t| ƒj|fi |¤ŽddS )NT)Z	full_prec)rC   r   Úevalf)re   ÚnÚoptions© rt   úN/var/www/auris/lib/python3.9/site-packages/sympy/solvers/tests/test_solvers.pyÚNS/   s    rv   c                  C   sö   t tdƒ\} }| tƒ|tƒ }}t|t d || d g|t|ƒ||d t| d iks\J ‚t||t  d ||gdd|d|digksŒJ ‚t||d t  t ||gdd|t|digksÀJ ‚t| dƒd td gddtd	| dƒdigksòJ ‚d S )
NZfgé   é   é   T©Údictr   é   éþÿÿÿ)Úmapr   ri   rF   rj   )ÚfÚgZfxZgxrt   rt   ru   Útest_swap_back3   s     ÿ04r   c              	   C   s.   zt | |ƒ W dS  ttfy(   Y dS 0 d S )NTF)rF   Ú	TypeErrorÚNotImplementedError)ÚeqÚsymbolrt   rt   ru   Úguess_solve_strategy=   s
    
r†   c                   C   s  t tdƒtƒsJ ‚t ttƒs J ‚t tt tƒs2J ‚t dt tƒsDJ ‚t ttdƒ tƒsZJ ‚t tdtddƒ  tƒsvJ ‚t td d tƒsŒJ ‚t td d tƒs¢J ‚t tt t tƒs¸J ‚t tttƒ t tƒsÒJ ‚t ttd  td tdtd  ƒ  tƒsJ ‚d S )Né   rw   r|   ry   )r†   r   ri   ra   r-   r   rj   r$   rt   rt   rt   ru   Útest_guess_polyE   s    $ÿrˆ   c                   C   sv   t ttƒd tƒsJ ‚t ttddƒ ttƒ d tƒs:J ‚t dt dttƒ  tƒsXJ ‚t tdt  t tƒsrJ ‚d S )Nr|   ry   r‡   )r†   r-   ri   r   rj   rt   rt   rt   ru   Útest_guess_poly_cvU   s    ÿr‰   c                   C   s€   t td td d  tƒsJ ‚t ttd  td tdtd  ƒ  tƒsLJ ‚t ttƒd ttddƒ ttƒ d  tƒs|J ‚d S )Nr|   rw   ry   )r†   ri   rj   r-   r   rt   rt   rt   ru   Útest_guess_rational_cv`   s
    $ÿrŠ   c                   C   sœ   t ttƒd tƒsJ ‚t dttƒ t tƒs0J ‚t ttƒtt ƒ t tƒsPJ ‚t dt d tƒsfJ ‚t dt  d tƒs~J ‚t ttt  t tƒs˜J ‚d S )Nr|   rw   ry   é
   )r†   r$   ri   r3   rj   ra   rb   rt   rt   rt   ru   Útest_guess_transcendentalk   s    ÿrŒ   c               	      sT	  t dtdi‰ t dt  d dt  dt  d f‰t‡ ‡fdd„ttttfD ƒƒsTJ ‚ttˆŽ t tƒˆ kslJ ‚ttt d d	 ƒƒt	dƒt	dƒ hks–J ‚tt t d
 t t d gƒt d	tdiksÂJ ‚tt t
t ƒ t ddt
t ƒgksæJ ‚tdƒtdt ƒ  krg ksn J ‚tddgƒg ks$J ‚ttdƒgt gƒg ks@J ‚ttdd„ ƒ ttdd„ ƒ tt t ttgddgkszJ ‚ttdd„ ƒ ttdd„ ƒ tt t ttgddgks´J ‚ttd
 thƒd
gksÐJ ‚ttd
 t thƒtd
igksòJ ‚tt t d
 t tgƒd
t tfgksJ ‚tt t d
 t tgddt d
t igksJJ ‚tt t d
 ƒt d
t igksnJ ‚tttt   d ttgƒtdtdiksšJ ‚ttt t  t t ttgƒtt ttiksÌJ ‚tt d  tt   t t t d d	t t  d	 t  } t| tttgtttgd}|tt dt  td	t t td  d	t  tdd	t  iksbJ ‚t| tttgdd|gks‚J ‚t| tttgddtttgt dt  dd	t  d	t t td  d	t  fhfksÜJ ‚t| tttgtttgddtt dt  td	t t td  d	t  tdd	t  iks8J ‚tt t  td  d ttf}t|Ž td tt   d t  tfgks‚J ‚ttt  td t d	   d
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t d
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t ƒt  t
tƒt fƒt tdƒ ttdƒ igks¢J ‚ttt
t ƒt  gt tƒtdƒ dfgksÐJ ‚tt d t tƒt d gksòJ ‚tg t gƒg ksJ ‚tt d d	 td ft tƒddgks2J ‚tt d d	 td ftt ƒddgks\J ‚tt d d	 t td t ftttt ddtttt gtttd td	t ƒ ftttd td	t ƒfhfksÌJ ‚tt t d d	 t t d gƒt t d igksJ ‚tt t d dt  dt  d	 fƒt t d iks:J ‚ttt d d ƒƒd gksXJ ‚tdtt dƒgt gddt digks‚J ‚ttt t ƒtt dƒtt t d ƒgt gddg ks¸J ‚ttt t d ƒt dk gt ƒrÚJ ‚ttt dƒt d dk gƒtt dƒksJ ‚ttt t ƒtt t d ƒgt ƒg ks,J ‚tdt ƒg ks@J ‚tt d dgt gddg tƒ fkshJ ‚tt t t d  d td t  t dt  gddd!t tgdt tft dfhfksÂJ ‚tttd t td
ƒt  fƒ ¡ ƒt tgksôJ ‚tt d t gtt fddtt gtƒ fk	s"J ‚tt d t gtt hddt tgtƒ fk	sPJ ‚d S )"Néýÿÿÿr|   rx   rw   é   rp   c                 3   s"   | ]}t |ˆƒttƒˆ kV  qd S ©N©rF   ri   rj   )Ú.0Ú	container©ÚansÚeqsrt   ru   Ú	<genexpr>{   ó    z"test_solve_args.<locals>.<genexpr>r‡   ry   éÿÿÿÿT©Zimplicité*   c                   S   s   t td td ftttƒS ©Nry   rw   r   rt   rt   rt   ru   Ú<lambda>‡   r—   z!test_solve_args.<locals>.<lambda>c                   S   s   t tttƒS r   ©rF   ri   rt   rt   rt   ru   rœ   ˆ   r—   ©Úexcluder   c                   S   s   t td td ftttƒS r›   r   rt   rt   rt   ru   rœ   Œ   r—   c                   S   s   t tttƒS r   r   rt   rt   rt   ru   rœ      r—   rz   ©ÚsetF)rŸ   Úsimplifyé   é   c                   S   s$   t ttƒttƒ ttƒ ttƒ ƒS r   )rF   r$   ri   r5   rj   rt   rt   rt   ru   rœ   ³   r—   )r}   rw   )rw   rw   )rw   r}   ç        )r¡   Úcheck)ri   rj   ÚallÚtupleÚlistr¡   Ú	frozensetrF   r   r   r$   r-   r_   Ú
ValueErrorra   rb   rc   rg   rh   rf   rƒ   r#   r   rk   r   Úkeys)r„   ÚsolÚargsrt   r“   ru   Útest_solve_argsw   sž    $
ÿ*,$("*.$,28D >ÿ
8ÿ
,2Fÿ
&ÿ.ÿÿ
."***
þÿ
68*6"*((.ÿÿ
2.r¯   c                  C   sÎ  t dt d tƒtddƒgks"J ‚t tdt dƒtƒtddƒgksFJ ‚tt td d tƒƒtj tjhksnJ ‚tt ttd dƒtƒƒtj tjhks˜J ‚t ttd  tƒtd gks¸J ‚ttdƒ} t ttd  tƒ| |  d t	dƒt
 |  d  |  d t	dƒt
 |  d  gksJ ‚tdƒ\}}}}}}t |t |t  | |t |t  | gttƒt|| ||  || ||   t|| ||  || ||   iks¦J ‚ttjttji}t tt tt fttƒ|ksØJ ‚t tt tt fttfƒ|ksüJ ‚t tt tt fttgƒ|ks J ‚tt td dt  d tƒƒddtj  tdƒddtj  hksfJ ‚tt td d d t tƒƒt	dt	tƒ ƒt	dt	tƒ ƒ t	dt	tƒ ƒt	dt	tƒ ƒ hksÊJ ‚d S )Nry   rw   r|   úa11,a12,a21,a22,b1,b2rp   r‡   r}   )rF   ri   r   r   r¡   r   ÚOnerj   r,   r-   r   r   ÚZeroÚHalfra   )ÚrxÚa11Úa12Úa21Úa22Úb1Úb2Úsolutionrt   rt   ru   Útest_solve_polynomial1ß   s:    "$(* 
:ÿ.  þÿ
"$$ýÿÿr¼   c                   C   s   t dtƒg ksJ ‚d S )Nr‡   r   rt   rt   rt   ru   Útest_solve_polynomial2  s    r½   c                   C   s´   t ttƒd tƒdgksJ ‚t ttƒd tƒdgks8J ‚t ttddƒ d tƒdgksZJ ‚t ttddƒ d tƒdgks|J ‚t ttƒttddƒ  ttddƒ  tƒdgks°J ‚dS )	zŽ
    Test for solving on equations that can be converted to a polynomial equation
    using the change of variable y -> x**Rational(p, q)
    r|   rw   r‡   r¤   ry   é   r   N)rF   r-   ri   r   rt   rt   rt   ru   Útest_solve_polynomial_cv_1a  s
    ""r¿   c                   C   sj   t tdt dtttƒ   tƒƒtjdtd  hks8J ‚t ttttdƒd  tƒƒtjtdƒhksfJ ‚d S )Nr‡   r|   rw   ry   r¾   )r¡   rF   ri   ra   r-   r   r²   r,   rt   rt   rt   ru   Útest_solve_polynomial_cv_1b  s    8rÀ   c                   C   sv   t tdt  d tƒtjttdƒ d  tjttdƒ d  gtjttdƒ d  tjttdƒ d  gfv srJ ‚dS )z‰
    Test for solving on equations that can be converted to a polynomial equation
    multiplying both sides of the equation by x**m
    r|   ry   rw   N)rF   ri   r   r³   r   r-   rt   rt   rt   ru   Útest_solve_polynomial_cv_2  s
    **ÿÿrÁ   c                  C   s  t d dt d   dt d   dt   d } t| dd	}|D ]&}|  t | ¡ ¡ ¡ }t|d
ƒs<J ‚q<t d dt d   dt d   dt   d } t| ƒ}|D ]}|jtksœJ ‚qœttt d dt d   d ƒd
 ddtt d dt d   d d
ƒ ¡ ksþJ ‚d S )Nrx   én   ry   é7   rw   i	  iÓ  F©r¦   r   rp   r‹   é   é   ©Úexponent)ri   rF   Úsubsrr   ÚtnÚfuncr[   rH   ©r   ÚsÚrÚresrt   rt   ru   Útest_quintics_1"  s    ,,	& ÿrÐ   c               
   C   s®  t d dt   d } t| dd}|D ]&}|  t | ¡ ¡ ¡ }t|dƒs$J ‚q$t d dt d   dt d   d	t   d
 } t| ƒ}|D ]}|jtks„J ‚q„tt d dt d   dt d   t  d ƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒgksªJ ‚d S )Nrx   rp   r£   FrÄ   r   ry   rw   r‹   rÅ   rŽ   r|   r‡   )ri   rF   rÉ   rr   rÊ   rË   r[   rÌ   rt   rt   ru   Útest_quintics_29  s     ,*,,,,,ûrÑ   c                  C   sF   t d t d  dtddƒ  } t| ƒt|  ƒ  kr<g ksBn J ‚d S )Nrx   ry   rw   r|   )ri   r   rF   ©rj   rt   rt   ru   Útest_quintics_3L  s    rÓ   c                  C   s>   t td dt  d ƒ} tdd„ | D ƒƒr6t| ƒdks:J ‚d S )NrŽ   rw   c                 s   s   | ]}t |tƒV  qd S r   )Ú
isinstancer[   ©r‘   Úirt   rt   ru   r–   T  r—   z&test_highorder_poly.<locals>.<genexpr>)rF   ri   r§   Úlen©r­   rt   rt   ru   Útest_highorder_polyQ  s    rÙ   c                   C   s<   t ttd  td tdtd  ƒ  tƒtd gks8J ‚dS )z!Test solve for rational functionsry   rw   r|   N)rF   ri   rj   r-   rt   rt   rt   ru   Útest_solve_rationalW  s    rÚ   c                   C   s&   t ttƒd t ƒdt gks"J ‚dS )z)Test solve for simple conjugate functionsry   N)rF   r    ri   r   rt   rt   rt   ru   Útest_solve_conjugate\  s    rÛ   c                   C   sˆ   t td td  ttddtt ittigks2J ‚t td td ttƒ  ttddtt tttƒƒ itttttƒƒ igks„J ‚d S )Nrw   Trz   )rF   ri   rj   r$   r-   rt   rt   rt   ru   Útest_solve_nonlineara  s    26ÿrÜ   c                  C   sl   t dƒ} tt| d d| d d   dd| d d   ƒ| ƒg ksDJ ‚tt| d|   d|  ƒ| ƒg kshJ ‚d S )Nri   rw   r|   r‡   )r   rF   r   ©ri   rt   rt   ru   Útest_issue_8666g  s    <rÞ   c                   C   s:   t ddtd  dt   d tƒtddƒtjgks6J ‚d S )Nr‡   rw   é   r   )rF   ri   r   r   r³   rt   rt   rt   ru   Útest_issue_7228m  s    rà   c                   C   s0   t ttd ƒttd ƒ tƒtdƒgks,J ‚d S )Nry   r‹   )rF   r%   ri   r-   rt   rt   rt   ru   Útest_issue_7190q  s    rá   c                  C   s<   t dƒ} | t| d d ƒ }| | ¡}t|| ƒg ks8J ‚d S )Nri   rw   r|   )r   r-   r   rF   )ri   r   Zf_diffrt   rt   ru   Útest_issue_21004u  s    
râ   c                  C   st   t dƒ} ttt| t| dƒ| dkB fƒdƒƒ}|dgks:J ‚ttt| t| dƒ| dkB fƒdƒ| dd}|du spJ ‚d S )Nri   r   r|   rØ   T)r   rF   r   r.   rQ   )ri   rÎ   rt   rt   ru   Útest_issue_24650|  s
    $*rã   c               	   C   s²  t dƒ\} }}}}t| d | | | d|  |d g| |gƒg ksDJ ‚t| d | | | d|  | d g| |gƒg ksvJ ‚t| d | d | | | d|  g| |gƒg ks¨J ‚t| d|  d d|  d|  d g| |ƒ| d|diksäJ ‚tdd||d  |d d dg|d |d d	| d |d  dgg d
¢gƒ}t|| |||ƒ| || d  | |d||| d  | iksrJ ‚t| | | | | | g| |||ƒ| | || iks®J ‚d S )Nzx, y, z, t, nr|   rw   rx   r   rŽ   rp   r   r}   )r˜   r   r|   r   r   )r   rF   r>   rI   )ri   rj   rk   rl   rr   ÚMrt   rt   ru   Útest_linear_system„  s    222<"þ*ÿ
rå   c                  C   sF   t g d¢g d¢g d¢g d¢gƒ} t| tttƒtdtdtdiksBJ ‚d S )N)r   g      .@ç      $@g     à…@)r|   r|   r|   g      Y@)r   ræ   g      @g      i@)g      Àr   r   r   r   g      NÀg      d@)r>   rI   ri   rj   rk   )rä   rt   rt   ru   Útest_linear_system_xfail˜  s    ýrç   c                  C   sš   t dƒ} t| ddƒ| ddƒ | ddƒ | ddƒ | ddƒ | ddƒ g| ddƒ| ddƒ| ddƒ| ddƒƒ| ddƒ| ddƒ | ddƒ| ddƒ iks–J ‚d S )Nra   r   r|   )r   rF   ©ra   rt   rt   ru   Útest_linear_system_function£  s    > ÿ&ÿré   c                  C   s2   dd„ } t ddƒD ]}| |ƒ\}}t||ƒ qd S )Nc           
         sÔ   d|  d }t ddd\‰ }}t d | ¡dd}t d | ¡dd}t d |d ¡dd}t‡ fd	d
„t|ƒD ƒƒ}g }t| ƒD ]L}	| | ˆ |	¡ ˆ |i¡||	  ¡ | | ˆ |	¡ ˆ |i¡||	  ¡ q~||fS )Nrw   r|   z	x, x0, x1T©Úrealzy0_:{}zy1_:{}zc_:{}c                 3   s   | ]\}}|ˆ |  V  qd S r   rt   )r‘   ÚoZcoeffrÝ   rt   ru   r–   ´  r—   zLtest_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqs.<locals>.<genexpr>)r   ÚformatÚsumÚ	enumerateÚrangeÚappendr   rÉ   )
ZwyÚorderÚx0Úx1Zy0sZy1src   Úexprr•   rÖ   rt   rÝ   ru   Ú_mk_eqs«  s    $&z9test_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqsr|   rß   )rð   rF   )rö   rr   r•   rc   rt   rt   ru   Ú(test_linear_system_symbols_doesnt_hang_1©  s    r÷   c               '   C   s  t g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d	¢g d
¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢gƒ} tdƒ }\}}}}}}}}	}
}}}}}}}}}}|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# |
td$ƒd |td%ƒ d |td&ƒ d |td'ƒ d( |td)ƒd( |td*ƒ d |td+ƒd, |td-ƒ d |td.ƒd  |td/ƒ d |td0ƒd i}t| t |d1 ƒ ƒ}t||ƒ|ksÔJ ‚td2ƒ}t||  t |d1 ƒ ƒ}t||ƒ|ksJ ‚d S )3N)éB   é   é'   é2   éX   é(   é%   é`   r¤   éA   é   é   rþ   éH   r¤   é   rÃ   rþ   é   éL   )r‹   é]   é"   éb   é;   é,   éC   éJ   r  é^   éG   é=   é<   é   rŽ   rw   é9   rß   é   éN   )r  é[   r  é   é@   r   rù   é5   éM   r  éU   é:   éW   rú   rú   rÆ   é$   r  r  ry   )r  éF   rp   r  éD   é+   éV   éS   éQ   r  é   é.   r  é   r
  r%  r  rú   é?   rŽ   )éE   rý   r  é   r  rý   r'  r  r  r  r&  éY   é>   r  é   é&   é   rÅ   r£   r$  )rû   é   r  r  r  é-   r  r  r  r  r  éc   éa   éR   rß   r&  r2  r  r   é#   )r  r/  r1  rü   r‹   r  é	   r  éZ   r4  r'  é)   r!  r$  r1  r#  r0  rü   rù   rú   )rš   r*  r  r   rŽ   é!   r  r$  r#  rp   r"  éK   r"  r'  r  r  r,  r  rÅ   rù   )rÆ   rß   rw   r  r  é4   rÿ   rx   é    é3   r  r  éO   rü   r%  r  r  é   r9  r  )r  r  r-  r  r$  rú   r(  r  r  r£   r¤   é1   rþ   rø   r.  r  ry   r  r  r=  )r  r4  éP   r@  r?  r  r|   rþ   rw   r  é6   r4  r?  é/   rB  r6  r5  r   r2  rý   )rp   r@  r4  r  r  r  r1  r%  r1  r3  rp   r	  é0   r;  rø   rù   r,  rB  r3  rþ   )r,  r  éI   r  r;  r"  r  r.  r   r  é\   r.  r3  r  r  r  r?  r7  r  r1  )rw   r<  r  rù   r  rþ   r%  r  rx   r8  r3  r   r  r  r   r1  r%  rü   r)  rû   )rý   é8   r|   r  r>  r	  r>  r,  rþ   r  r1  rC  ry   r|   r<  r  r	  r5  éT   r<  )r9  rp   r  r>  r   r6  é   r(  rù   r  r&  r  r  rÅ   r  rÿ   rH  r  r  r|   )r3  r/  r£   r;  r|   rw   rû   rI  r;  r  r  r4  r8  rE  r=  r>  r  ry   r4  rÿ   )rý   r  r;  r‹   r‹   r  rG  r  r4  rx   r  rD  r|   r?  r¤   r/  rû   r  r"  r;  )r.  r+  r#  r!  r  r;  r7  r  r  r   r  rÅ   r$  rü   rD  rÿ   rü   r  rI  ry   zx:19l	   ³fœX·j"Ìbµ!SBs= l	   Ì0e7HPÈég%Oï0 l   B>é tsypYÎ/l   s LYÀr%ú9És;Ll   eAnA²&d%â$ÌI%%l	   æ ˜2$(äJôs’gw l   ydx#ZçcCj×GæY_l	   ˜`Jn ‘+ÒOKßa l	   I\<ße:‘B	W9òP l	   È
 _J²a³woâZ% l	   :îN1âS:leÛ)ÀB l	   d/%ÙpYA»7qmÎ l	   m:.v,¦&WCa0 l   àxmK¤qe@ Agd5l   Ÿ[ioäšzkÄz« l	   NƒnÚ:!=ƒEùl2 l	   [R!`ª8rq§wÛ„+Ò l	   [fîPîo/”kš#8o	 l	   ëKºdLJ¤w0jG3Y)9r l	   ²È„Rlx¬`Ý[¸6gI l	   vJ²¦1¨vÐBT l   x™c°ykiö&õ_#Ol   ¿)à]’y½RH-®-TWl   ¨IÄS·ððsÔf
rWl   
…t‰[T”Fl	   ñ\CQâæl2ñGÝBª3 l	   1]* À}ŽcûÂkkw l	   ]bSE:_jVÒH}†S ©r|   rj   )r>   r   r   r©   rF   r   )rä   Úsymsró   rô   Úx2Úx3Úx4Úx5Úx6Úx7Úx8Úx9Úx10Zx11Zx12Zx13Zx14Zx15Zx16Zx17Zx18r­   r•   rj   rt   rt   ru   Ú(test_linear_system_symbols_doesnt_hang_2Æ  s^    í2írU  c               
   C   s–   t dƒ} tg d¢ddd|  dgdd| d dggƒ}t|tttgƒtd| d d	|    tdd
|  | d d	|     td|  | d d	|    iks’J ‚d S )Nrr   )r|   rw   r   r|   r|   ry   rw   r‡   r˜   r   r/  r£   rŽ   )r   r>   rJ   ri   rj   rk   )rr   rä   rt   rt   ru   Útest_linear_systemLUý  s    *"þrV  c                     sd  ddl m} m} tttƒd tƒtdƒgks0J ‚tt| t | ttƒd  tƒƒ| |  tdƒhkshJ ‚tttƒt	 tƒt
t	ƒ dt  t
t	ƒgks˜J ‚tdttƒ t	 tƒt
t	d ƒ dt  t
t	d ƒgksÔJ ‚ttttƒttƒƒtƒtd gksúJ ‚ttttƒtt ƒ t	 tƒƒtt	d tt	d d ƒd  ƒtt	d tt	d d ƒd  ƒhtt	tt	d d ƒ ƒtdƒ tt	tt	d d ƒ ƒtdƒ htt	d tt	d t	d  ƒd  ƒtt	d tt	d t	d  ƒd  ƒhfv sæJ ‚tttƒd tƒtdƒgksJ ‚ttttƒdƒtƒtdƒgks,J ‚tttƒd tƒtdƒgksNJ ‚ttdt ƒd tƒtddƒgksvJ ‚tdtd  tƒg ks’J ‚tddt  tƒg ks®J ‚ttdt  tƒttdƒƒ tdƒ gksÞJ ‚tdt d tdt d ƒ tƒtddƒtdttddƒƒ d ƒd  gks0J ‚tdt tdt ƒ tƒttddƒƒd gksdJ ‚ttdt d	 d	ttƒ  tƒƒtd
ƒtd	ƒtt  hks¤J ‚dtdt d ƒ d ‰ tˆ tƒ}t|ƒdkrìt‡ fdd„|D ƒƒsðJ ‚tdtdt d ƒ d tƒttddƒƒd d gks,J ‚tttƒd tƒtt gksNJ ‚ddt d d  dddt d    ‰ tˆ tƒ}tdƒ }dtddƒ }tdd| d  ƒ}tdƒ}tdƒ}|t|d ƒ }	|d }
ddtdƒ  }| }|t|d ƒ }|d }||dt||	 |
  ƒ   ||dt||	|
  ƒ   ||dt|||  ƒ   ||dt|||  ƒ   ||dttdd| d  ƒ ƒ   g}||ks¦J |ƒ‚tˆ  ¡ tƒ|ks¾J ‚ttttƒ t	 tƒt
t	t ƒ dt  t
t	t ƒgksüJ ‚tttdt ƒ t	 tƒt
t	t ƒ d t t
t	t ƒd gksBJ ‚tttttƒƒ t	 tƒttt
t	t ƒƒ tt
t	t ƒdt  ƒt tt
t	t ƒdt  ƒ tt
t	t ƒƒgks¸J ‚ttttƒ tƒtd ttddƒ gksæJ ‚tt	|t | t   tƒ|  t	 t	|  g| t	 |t	  gfv s,J ‚tt	|t| t ƒ  tƒ| tt	| ƒ gks^J ‚tt	|d| t    tƒ|t	 | t	  gt	| | t	   gfv s¤J ‚tt	| t|   tƒt	|  d|  gksÒJ ‚ttt t	 tƒtt	ƒttƒ gksüJ ‚tdt d tƒdtdƒtdƒ  gks*J ‚ttt	 ƒtdit	digksLJ ‚ttt	 gƒtdit	digkspJ ‚ttt	 d ƒtdit	digks–J ‚ttt	 d gƒtdit	digks¾J ‚ttt	 td t	d   ƒtditt	 itt	it	digksþJ ‚ttt	 td t	d   gƒtditt	 itt	it	digk	s@J ‚tttdƒt ƒdt  tƒdgk	sjJ ‚tttdƒt ƒttdƒt ƒ tƒdgk	sœJ ‚tdƒ‰tt	ˆtdƒt ƒ t	ˆtdƒt ƒ  tƒdgk	sÞJ ‚tˆtƒˆdƒ tƒdgk
s J ‚tˆtƒˆdt ƒ tƒdgk
s&J ‚tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ ttdd„ ƒ ttdd„ ƒ ttttƒƒƒdtd gk
s¬J ‚tdddd\} }ttt| d tt| ƒd  ƒ|ƒƒd!k
sìJ ‚tt	dt  t tƒtt	ƒttƒ gksJ ‚tdt ƒtdt ƒtttd  ƒfD ]N}tttƒtdƒd  |t	 gƒ}|d t	 |d t	  js@J ||fƒ‚q@ttd"t ƒtj ƒtd# td$ gks¼J ‚tttd"t	  ƒd tƒd"t	 d"t	 dt  gksôJ ‚tttt	 t ƒd tƒt	 t t	 t dt  gks0J ‚ttttd  ƒƒt d dt d gks`J ‚d S )%Nr   ©ra   rb   ry   rw   r‡   r¤   rx   iíÿÿÿrß   éüÿÿÿc                 3   s&   | ]}ˆ   t|¡jd ddkV  qdS ©T)Zchopr   N©rÉ   ri   rr   ©r‘   ra   ©r„   rt   ru   r–   *  r—   z,test_solve_transcendental.<locals>.<genexpr>r|   rŽ   rÆ   r6  ia	  rÅ   r‹   r   c                      s   t ˆ ttƒˆ ddƒ tƒS ©Nr|   rw   r   rt   ©r   rt   ru   rœ   f  r—   z+test_solve_transcendental.<locals>.<lambda>c                      s   t ˆ ttƒˆ dt dƒ tƒS ©Nrw   r   rt   r^  rt   ru   rœ   g  r—   c                      s   t ˆ ttƒˆ dt ƒ tƒS ©Nr|   r   rt   r^  rt   ru   rœ   h  r—   c                      s   t ˆ ttƒˆ dƒ tƒS r`  r   rt   r^  rt   ru   rœ   i  r—   c                   S   s0   t ttƒtttƒƒ ttƒtttƒƒ  d ƒS ©Nry   )rF   r(   ri   r'   rt   rt   rt   ru   rœ   o  s    c                   S   s   t td t t d tƒS ©Nrw   ry   r   rt   rt   rt   ru   rœ   s  r—   za, bTF)rë   Únegativeç      à?zP[2.0 - 0.318309886183791*acos(1.0 - 2.0*a), 0.318309886183791*acos(1.0 - 2.0*a)]éè  i¸  éX  ) Ú	sympy.abcra   rb   rF   r$   ri   r%   r¡   r3   rj   r/   r   r   r5   r-   r   r#   r   r   r×   r§   Úexpandrk   r0   r   r_   rƒ   r«   r   ÚstrÚis_Rationalr³   )ra   rb   r”   Úresultró   rô   rL  rM  rN  rO  rP  rQ  rR  rS  rT  Úyir­   rt   )r„   r   ru   Útest_solve_transcendental
  sÆ     80<&þþ""þú	"$"(0 (ÿ
4@
*<"(

$ü>F,&þ.F2F.*."$&(@B*2:"&""ÿ
.* ,,8<rm  c                  C   s  t dƒ} tdƒ| ƒ}tdƒ| ƒ}tdƒ\}}}}}}t|| ||  | || ||  | g||ƒ}	|	||| ||  || ||   ||| ||  || ||   iks°J ‚t|d |ƒdgksÈJ ‚td| d |ƒtddƒgksêJ ‚t|| | ¡ || | ¡  | || | ¡ || | ¡  | g| | ¡| | ¡ƒ}	|	| | ¡|| ||  || ||   | | ¡|| ||  || ||   iks˜J ‚t| | ¡d | | ¡ƒdgks¾J ‚td| | ¡ d | | ¡ƒtddƒgksîJ ‚d| d d| d h}
t|
||hƒ|tddƒ|diks,J ‚t dƒ}td	ƒ}|d ||ƒd  d|  d }t| |¡t||ƒ|ƒƒ| d ||ƒ gksJ ‚t dƒ}tdƒ| ƒ}t|| || | ¡  | || || | ¡  | g|| | ¡ƒ}	|	| | ¡|| ||  || ||   ||| ||  || ||   iks:J ‚t dƒ}td	ƒ}t||ƒ |¡||ƒ |d¡ d ||ƒ |¡||ƒ |d¡ g||ƒ |¡||ƒ |d¡ƒ}	|	||ƒ |d¡tdƒd ||ƒ |¡tdƒd iksäJ ‚t||ƒ |d¡||ƒ |d¡ d d||ƒ |d¡ ||ƒ |d¡ d||ƒ |d¡ g||ƒ |d¡||ƒ |d¡ƒ}	|	||ƒ |d¡d
||ƒ |d¡diksŒJ ‚d S )Nrl   ri   rj   r°   r|   ry   rw   r‡   r   r   )r   r   r   rF   r   r   r   )rl   ri   rj   rµ   r¶   r·   r¸   r¹   rº   ÚsolnÚeqnsr   ÚFrt   rt   ru   Ú$test_solve_for_functions_derivatives  sn    0  þ
",ÿÿÿ(&ÿ&0& 4 ÿÿ
ÿ( ÿ@ÿ<6ÿÿÿrq  c                  C   st   t dƒ} td | tƒd  dt  d }| t¡}t|| tƒ t¡ƒdt | tƒ gtd | tƒ  gfv spJ ‚d S )Nr   rw   r‡   r|   )r   ri   r   rF   )r   rp  re   rt   rt   ru   Útest_issue_3725À  s     
rr  c               	      sà  t dƒ\} }}}tdd| |||gƒ}tddg d¢ƒ}tddg d¢ƒ}t|| | | |||gƒ| d|tddƒ|d|diks|J ‚t|| | g| |||gƒ| d|tddƒ|d|diks¶J ‚tt|| |ƒ| |||gƒ| d|tddƒ|d|diksðJ ‚t|| ||  g| |||gƒ| ||tddƒ| iks,J ‚t|| ||  g| |||gƒ| || |tddƒ| ikslJ ‚t|| ||  || ||  g| |||gƒ| ||d	|d	iks°J ‚tt|| || ƒg| |||gƒ| ||tddƒ| iksîJ ‚tt|| || ƒg| |||gƒ| || |tddƒ| iks0J ‚tt|| || ƒt|| || ƒg| |||gƒ| ||d	|d	iksxJ ‚t d
ƒ\}}td||ƒ}td|dƒ‰td|dƒ}|ˆ | }	|	j|	 }
|
 ˆ¡‰ tt	‡ ‡fdd„ƒ d S )Núa b c drw   )r   rw   r   r   )r|   rw   ry   r‡   r|   r˜   ry   r}   r   zm nÚAri   rb   c                      s
   t ˆ ˆƒS r   )rF   rt   ©Zgrad_fri   rt   ru   rœ   â  r—   z#test_solve_Matrix.<locals>.<lambda>)
r   r>   rF   r   r   r?   ÚTr   r_   r«   )ra   rb   rc   rd   rt  ÚBÚCrn   rr   rÎ   r   rt   ru  ru   Útest_solve_MatrixÇ  s*    8::<@D>BH

ry  c                  C   sV  t dƒ} tttƒdksJ ‚tttgddks0J ‚tt| gddksFJ ‚tttdt  ƒttd ftdt ffv stJ ‚tttdt  tgdtdt fksœJ ‚tdt t dƒttd ftdt ffv sÊJ ‚tdt t dtgƒttd fksðJ ‚tdt t dtgƒtdt fksJ ‚ttd t dƒttd fks<J ‚t| tƒ| tft| ffv s\J ‚tttƒd ttƒd  d t ƒtd	ttƒd  ttƒd  fks¦J ‚tttƒd ttƒd  d t tgddksÚJ ‚tttdƒƒtdfksöJ ‚tddt d  ƒd
ksJ ‚ttd tt ƒ tgdtdfks>J ‚ttd ttƒ tgdtd ttƒ dfksrJ ‚ttttd  ƒ tgdtdfksœJ ‚tdt d ƒdt d dfksÂJ ‚tddtd   ƒtdfksäJ ‚tttƒd  tttƒd   t }t|ƒdksJ ‚ttƒd ttƒd  }t|ƒdksDJ ‚tt	dd„ ƒ d S )NÚw©r   r|   rž   ©r   rw   ry   r   r|   r}   ©r   r   r˜   c                   S   s   t ttdƒdƒS ra  )rG   r   ri   rt   rt   rt   ru   rœ   ÿ  r—   z#test_solve_linear.<locals>.<lambda>)
r   rG   ri   rj   r3   r5   r   r$   r_   r«   )rz  r„   rt   rt   ru   Útest_solve_linearå  s6    .(.&($ "ÿ
4*4*&"$r~  c                  C   sb  t ttd  ttd   tt  dt t  t d tttgtƒtdtdtdiksVJ ‚t tt ttd   dt d td t   ttgtƒtdtdiksžJ ‚t td t td  td t td   td t t  td d t t  td d  td  tttgtƒtdtdtdiks"J ‚ttt ttt    } }}t|  t|  t|  |  d|  d|  }tttf}ttf}t ||ƒtdtdtdiksœJ ‚t |||ƒtdtdtdiks¾J ‚t ||g|¢R Ž tdtdtdiksæJ ‚t tt t d tgƒg ksJ ‚t td t dt  tgƒtditdigks:J ‚t dtgƒg ksPJ ‚t dtgdd	g ksjJ ‚t dtgdd
g i fksˆJ ‚t dtgƒg ksžJ ‚tt dt  t d }tth}t ||tƒtdtdiksÜJ ‚t ||tdd
ttgdhfks J ‚t ttt ƒtdt ƒ tfƒd u s*J ‚t tt tt  dt  ttfƒtdt iks^J ‚d S )Nrw   r|   r}   r˜   ry   r‡   r   Trz   r    )rw   ry   )rK   ra   ri   rb   rc   rj   r5   )ÚXÚYÚZr„   ÚcoeffsrK  ZabeqrÍ   rt   rt   ru   Útest_solve_undetermined_coeffs  sj    <ÿþÿÿ
ÿ&ÿÿ
ÿÿ
ýü
,
ÿ
ÿÿ"ÿ$*rƒ  c               
   C   s   t dƒ} ttj| k | tk ƒ}t| d dkƒ|ks4J ‚t| d dkgƒ|ksNJ ‚t| d dkg| ƒ|ksjJ ‚t| d dkg| gƒ|ksˆJ ‚t| d d dƒt| d d dƒg}t|ƒttttt	dƒ | ƒt| dƒƒttd| ƒt| t	dƒƒƒƒt
ddƒƒksüJ ‚t ddd} t| d d dƒt| d d dƒg}t|ƒtttt	dƒ | ƒt| dƒƒttd| ƒt| t	dƒƒƒƒksrJ ‚t| d | d  dk | ƒttd| ƒt| dƒƒks¨J ‚t| | d  dk| ƒttt | ƒt| dƒƒksÜJ ‚tt| ƒtjkƒttd	 | k | ttd
d	ƒ k ƒksJ ‚tt
d| dk ƒƒtj| k| tk @ ks>J ‚tt
d| dk ƒƒt | k | dk @ kshJ ‚tt
| dk dƒƒtj| k| tk @ ks’J ‚tt
| dk dƒƒt | k | dk @ ks¼J ‚tt
d| ƒƒdksÔJ ‚tt
d| ƒƒdgksîJ ‚tt
d| ƒƒdksJ ‚tt
d| ƒƒdgks J ‚tt
d|  ƒƒdks:J ‚tt
d|  ƒƒdksTJ ‚ttd| ƒƒdkslJ ‚ttd| ƒƒ| t k| tk @ t| dƒ@ ksœJ ‚d S )Nri   r|   rw   r   r˜   Trê   ry   rŽ   rx   F)r   r<   r   r²   r   rF   r   r   r=   r-   r   r5   r³   r   r   r±   r   )ri   r­   Úsystemrt   rt   ru   Útest_solve_inequalities*  sD    $ÿÿÿ$6ÿ
648****r…  c               	      sÒ  t dt ƒg ksJ ‚t tddt   ƒdgks2J ‚t tttƒ d ƒdgksPJ ‚t dt  dt d  ddt   ƒg ks~J ‚t td  dt  td d  d ƒg ks¬J ‚t ttd  d d ƒg ksÌJ ‚t tttd d ƒ tƒdgksðJ ‚t ttƒt tƒttƒgksJ ‚t ttƒƒg ks(J ‚t td t ttƒd  ttƒd  d tƒddgddgfv slJ ‚dddt d   d	 ‰ t ˆ tƒ} t| ƒdkr´t	‡ fd
d„| D ƒƒs¸J ‚t ttd ƒtd ttƒ  ttddttgttttƒttd ƒ ƒfttttƒttd ƒ ƒ fhfks(J ‚t td t
d  t
d td   ƒtt ittit
digksjJ ‚t td ddtd    ƒg ksJ ‚t ttt
  t tƒdgks²J ‚ttdd„ ƒ ttdd„ ƒ d S )Nr|   rx   rw   ry   r}   r   r˜   r‡   rÆ   c                 3   s&   | ]}ˆ   t|¡jd ddkV  qdS rY  rZ  r[  r\  rt   ru   r–   ^  r—   z"test_issue_4793.<locals>.<genexpr>Tr    c                   S   s   t ttƒttƒ tƒS r   )rF   r%   ri   r$   rt   rt   rt   ru   rœ   e  r—   z!test_issue_4793.<locals>.<lambda>c                   S   s   t dt ttƒ d ƒS rb  )rF   ri   r$   rt   rt   rt   ru   rœ   f  r—   )rF   ri   r-   r$   rj   r%   r5   r3   r×   r§   rk   r_   rƒ   ©r”   rt   r\  ru   Útest_issue_4793Q  s,    .. $"D
*&8þB&"r‡  c                  C   s<  t ttƒƒt ttd ƒƒ  kr*dgks0n J ‚t ttd ƒƒdgksJJ ‚tdƒ} t d|  ttƒ tƒg kspJ ‚t dt td  d tƒdgks”J ‚tt td dt   t¡ƒƒtjtdƒhksÄJ ‚td	ƒ}t dd
t |tƒ  |tƒ |tƒƒtt	d
dƒ gksJ ‚t dt
d
t d
ƒ d tƒt	ddƒgks6J ‚t ttƒtttƒƒ d ƒt	ddƒtdƒd  d gkstJ ‚tt ttttƒƒttt ƒƒ d ƒƒƒttdƒ d d ƒttdƒd d ƒhdttdƒ d ƒ dttdƒd ƒ htdtdƒ d ƒtdtdƒ d ƒhfv sJ ‚tt tttƒtt ƒ d ƒƒƒttdƒ d ƒttdƒd ƒhkshJ ‚tt tt tdt   d tƒƒt	ddƒtd
ƒd  dt  t	ddƒtd
ƒd  dt  hksÌJ ‚t ttt ƒtt t ƒ d tƒtt tdƒ gksJ ‚t tt tt  d tƒtdƒttƒttƒ  gtdƒttt ƒ gfv sXJ ‚tj}t tdt ƒtdƒ tƒdt|t	ddƒtdƒt d   ƒt|t	ddƒtdƒt d   ƒgdt| d tdƒ| t d  ƒt| d tdƒ| t d  ƒgfv s
J ‚tddd}t d| d |d  ƒg ks8J ‚d S )Nry   r   r|   ra   r   rw   rÆ   rI  r   rx   r6  i´~ûÿi©æ  r‡   r˜   r'  rX  rh   T©Úpositive)rF   r-   ri   r   r¡   r   r   r²   r   r   r,   rA   r$   r%   rj   rk   ÚExp1r   )ra   r   r   rh   rt   rt   ru   Útest_PR1964i  sF    0$0<.>(((&ýÿ
  ÿ
 :ÿ
<ÿ.ÿ
DDþr‹  c                  C   s  t ddd} t| d d | ƒg ks&J ‚t dddd}t|d |d  d| d  |ƒdgks`J ‚t ddd} t d	ƒ}t| d
|  d d|  d|  d g| |ƒg ks¨J ‚t| | d|d  g| |ƒtdƒtdƒ fgksÜJ ‚t d	dd}t| d |d t| ƒ  || dd|| t| d ƒ igks(J ‚tddd\} }}t|d | d  |d |d  t| ƒ  || |dd|| t| d ƒ igksŒJ ‚d S )Nri   Trê   rw   r|   rr   ©Úintegerr‰  rˆ  rj   rx   r   rŽ   rp   rz   zx y z)r   rF   r-   r$   r   )ri   rr   rj   rk   rt   rt   ru   Útest_issue_5197–  s    ,44@rŽ  c                   C   s¸   t ttttt   tddƒttƒtjttƒ hks8J ‚t ttttt   tddƒttƒttƒ hkslJ ‚tddt d  dtd  d fƒg ks˜J ‚tddt d  ƒg ks´J ‚d S )NFrÄ   Tr|   rw   ry   )r¡   rF   ri   rj   r-   r   r²   rt   rt   rt   ru   Útest_checking¨  s    ÿÿ4,r  c               	   C   s€  t ttd d ƒd ƒtdƒtdƒ gtdƒ tdƒgfv s@J ‚t dttd t ƒ d td d  tƒtttdtt tdƒ  ƒ ƒ tttdtt tdƒ  ƒ ƒgks°J ‚tdƒ\} }t	dƒ}t | |td   t|tƒ ƒ |tƒƒttd | td  |  ƒgksJ ‚t
dƒ}tj}t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv sŽJ ‚t t|d	 td  ƒ| tƒtd
|d	  ƒ td
|d	  ƒgtd
|d	  ƒtd
|d	  ƒ gfv söJ ‚t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv sfJ ‚t |d d t|t ƒt|t ƒ  tƒt d|  gks¦J ‚t dt|t ƒt|t ƒ  tƒtdƒ| gksÜJ ‚tt dt|t ƒt|t ƒd   tƒƒtdtdƒ ƒ| ttdƒ d ƒ| ttdƒ d ƒ| tdtdƒ ƒ| hks\J ‚t ttƒd ƒtdƒgks|J ‚d S )Nrw   r|   rx   rp   zC1 C2r   ra   r‡   r   r˜   ry   r}   )rF   r-   ri   r$   rj   r%   r   r   r   r   r   r   rŠ  r5   r3   r(   r'   r¡   r1   r6   )ZC1ZC2r   ra   r   rt   rt   ru   Útest_issue_4671_4463_4467²  s>    &ÿ
(>ÿ
L$$þ  þ$$þ@6(&&ÿÿ
r  c               	   C   sL  t dƒ\} }tt| td  td  t|ƒtt  gttgƒƒt| t|ƒd  ƒ dt| t|ƒd  ƒ t|ƒ ft| t|ƒd  ƒt| t|ƒd  ƒt|ƒ fhks¨J ‚tttƒt	tƒ dt d gttgƒt
t	tddƒƒƒtddƒfgksðJ ‚tttƒt	tƒ dttƒ d gttgƒt
t	t
dƒƒ ƒt
dƒ fgks>J ‚ttttƒt	tƒ td d gttgƒƒt
t	dƒ ƒtdƒ ft
t	dƒƒtdƒfhksšJ ‚ttƒd t	tƒ td  dttƒ d g}t|ddttgt
dƒ ttdt ƒ t	t
dƒƒ ƒft
dƒ ttdt ƒ t	t
dƒƒ ƒ fhfks2J ‚t|ttddttgtttdt ƒ t	tƒ ƒftttdt ƒ t	tƒ ƒ fhfksŽJ ‚tt|ttƒƒt
ttd  t	t
dƒƒ ƒ ƒt
dƒ ft
td  t	t
dƒƒ ƒd t
dƒ fhksöJ ‚tt|ttƒƒt
dƒ ttdt ƒ t	t
dƒƒ ƒ ft
dƒ ttdt ƒ t	t
dƒƒ ƒfhks^J ‚ttƒd t	tƒ t dttƒ d g}t|ddttgt
dƒ tdt ƒ t	t
dƒƒ fhfksÆJ ‚t|ttddttgttdt ƒ t	tƒ fhfks J ‚tt|ttƒƒt
tt t	t
dƒƒ ƒ ƒt
dƒ ft
t t	t
dƒƒ ƒd t
dƒ fhks`J ‚t|ttƒtdt ƒ t	t
dƒƒ t
dƒ fgks˜J ‚tttd td  ƒtd	ƒ tt d fddttgtjtdƒftdƒtjfhfksòJ ‚ttttd td  ƒtd	ƒ tt d fttƒƒtjtdƒftdƒtjfhksHJ ‚d S )
Nzr,trw   r˜   r|   ry   r‡   Tr    r‹   )r   r¡   rF   ri   rj   r6   r-   r3   r$   r5   r%   r   r   rk   r±   )rÎ   rl   r•   rt   rt   ru   Útest_issue_5132Ï  sr    02ÿ.þÿ$ÿ(ÿ
(*ÿ
,
&(þÿ
<þ(&þÿ
(&þÿ
("ÿ ÿ$"þ
$ÿ
. ÿ2ÿr‘  c                  C   s´   t dƒ\} }}d}d}| dt  |dtd   t  |t d t  |dtd   t dt  |t  tt | g}tt|g}tt||dddƒdksšJ ‚tt||ƒƒdks°J ‚d S )Núlam a0 concç{®Gázt?çÌ«¢Ã;Êç?rw   r|   T)ÚmanualZminimal©r   rj   ri   r×   rF   ©ZlamZa0Zconcra   rb   r•   Úsymrt   rt   ru   Útest_issue_5335û  s    ."
þ
r™  ZHangsc                  C   sœ   t dƒ\} }}d}d}| dt  |dtd   t  |t d t  |dtd   t dt  |t  tt | g}tt|g}tt||ddƒdks˜J ‚d S )Nr’  r“  r”  rw   r|   F©Zrationalr–  r—  rt   rt   ru   Ú_test_issue_5335_float  s    ."
þ
r›  c                   C   sH   t ttd t d gtgƒƒtt d ƒ ftt d ƒfhksDJ ‚d S )Nrw   r‡   )r¡   rF   ri   rj   r-   rt   rt   rt   ru   Útest_issue_5767  s     ÿrœ  c                  C   s  t dddd\} }}}}}t dddd\}}}t dddd}	dtdƒd  ttdƒd   | tdƒd	 td |	d    d
|tdƒd   |	tdƒd    dtdƒd  ttdƒd   | d|tdƒd   |	tdƒd     }
dtdƒ t d }|
||	fS )NzD, R, H, B_g, V, D_cT)rë   r‰  zSigma_f, Sigma_a, nuri   rw   ry   iÁ‡ i'  rŽ   r|   rß   rÆ   éd   iá  )r   r   r   r-   )ÚDro   ÚHZB_gÚVZD_cZSigma_fZSigma_aÚnuri   r„   Úexpectedrt   rt   ru   Ú_make_example_24609  s    >"ÿFþÿr£  c                  C   sP   t ƒ \} }}t| |dd|gks$J ‚t|  ¡ |ƒ\}t|| ¡  ƒdk sLJ ‚d S )NT©r¢   g›+¡†›„=)r£  rF   rr   Úabs)r„   r¢  ri   Z	solapproxrt   rt   ru   Útest_issue_24609'  s    r¦  c                  C   s(   t ƒ \} }}tt| |ƒƒ|gks$J ‚d S r   )r£  r×   rF   )r„   r¢  ri   rt   rt   ru   Útest_issue_24609_xfail/  s    r§  c                   C   sê   t ttd dt  d tt d gttgƒƒtjtdƒfdtdƒ dtdƒ fdtdƒ dtdƒ fhksnJ ‚ttd t d td t gƒg ks–J ‚ttd t d tt d gttfƒttd t d tt d gttfƒksæJ ‚d S )Nrw   ry   r|   rx   r‡   )r¡   rF   ri   rj   r   r±   r-   rt   rt   rt   ru   Útest_polysysD  s    ,"ÿÿ(,ÿÿ
ÿÿr¨  c            	   
      sÆ  t tdd„ ƒ t tdd„ ƒ tdtd‰‡fdd„} ‡fdd	„‰td
ƒd u sPJ ‚| tttƒƒtg fƒsjJ ‚| tttƒd
 ƒtd
 g fƒsŒJ ‚| tttƒttdƒ d ƒˆd ˆd  d ˆˆd t gfƒsÐJ ‚| tttƒttdƒ d ƒtd d g fƒsJ ‚| tttƒtd
 td
dƒ  ƒtd td
 d  g fƒs@J ‚| tttƒttd
 ƒ tdt ƒ ƒdtdƒ t dt  d
 g fƒsŒJ ‚| tttƒttd
 ƒ d ƒdt d g fƒsÀJ ‚| tttƒttd
 ƒ td
t ƒ ƒdtd  dt  g fƒsJ ‚| tt	ttƒ t
ttƒ  tttƒ  tttƒ  ƒt	ttƒ t
ttƒ  d tttƒ tttƒ  d  g fƒs|J ‚| tttƒtd
t ƒ ƒdt d
 g fƒs¬J ‚| tttƒtd
t ƒ d ƒtd t d g fƒsäJ ‚| tttƒtd
t ƒ tdt ƒ ƒdtd  dt  d
 g fƒs,J ‚tttƒtd
t ƒ tdt ƒ d ƒdtd  dtd   dtd   dt  d g fdtd  dtd   dtd   dtd   d g ffv sÆJ ‚tttƒtd
t ƒ tdt ƒ td
dt  ƒ ƒdtd  dtd   d td   d!t  d g fks4J ‚| tttƒttd
 ƒ ƒtjg fƒs^J ‚ttƒttd
 ƒ td
ttƒ ƒ }| t|ƒdtd  dt  g fƒsªJ ‚tt|d"d#ƒtjtddƒhksÐJ ‚t|ƒg ksâJ ‚ttttƒttd
 ƒ td
ttƒ ƒ ƒƒtjtddƒhks$J ‚| tttƒttd
 dƒ dttƒ  tƒtd$ƒg fƒs`J ‚| tttd
t  ƒtd
 td
dƒ  ƒtd td  td  dtd   t d
 g fƒs¾J ‚| tttd
t  ƒdttƒ  tƒdt t t dt  g fƒsJ ‚| tttƒtd
t ƒ d tƒtd t d g fƒs>J ‚tttttd ƒƒƒdgks`J ‚tttttd ƒ dƒƒdgks†J ‚ttd
ttdt d ƒ ƒƒg ks®J ‚ttttdt d ƒd tƒƒƒtj tdƒhksæJ ‚ttttdt d
 ƒttd ƒ dƒƒƒtdƒtd%ƒhks&J ‚ttttd& ƒd tdt ƒƒƒd'gksTJ ‚tdt d td
dƒ d ƒdgks~J ‚tttd
 ttd dtd   t dƒ ƒƒtd(dƒtd(dƒhksÆJ ‚tttdtd  d& ƒdt  ƒƒtdƒ tdƒhksJ ‚ttdt d ƒttd
 ƒ ttd ƒ ƒd)gks:J ‚tttd ƒtdt d
 ƒ dttd
 ƒ  ƒdgksvJ ‚tttƒttd& ƒ d* ƒdgksžJ ‚tttd ƒttƒ d ƒdgksÆJ ‚ttdtd  d ƒdt d  ƒd)gksöJ ‚tttƒd d ƒd+gk	sJ ‚tttd ƒttƒ d ƒg k	s<J ‚tttd
 ƒt d& ƒd,gk	s`J ‚tttd ƒd ƒd-gk	s€J ‚ttd.t ttd d ƒ ƒd& ƒdgk	s°J ‚tttƒttd
 ƒ tttƒƒ ƒg k	sÞJ ‚tdt d
 ƒttƒ tdd
t  ƒ }t|ƒd) }t|ƒg k
s$J ‚t|ƒg k
s6J ‚t|dt  ƒtd(d/ƒgk
sXJ ‚t|dt  ƒg k
srJ ‚tttd
 dƒttdƒ ƒtd td  dtd   dt  d
  g fk
sÂJ ‚| ttttdƒ ttdƒd  ttƒ tƒˆd ˆd  ˆ ttƒ ˆˆd t gfƒs J ‚| tttƒttdƒ t ƒˆd ˆd  t ˆˆd t gfƒsfJ ‚tttƒttdƒ d ƒd
gksŒJ ‚t td0d„ ƒ t td1d„ ƒ tttttdƒ ƒttt dƒ tƒtttd
dƒ t tddƒ  gksöJ ‚| tttƒttd
 dƒttd ƒ  d ƒˆd, dˆd   d2ˆd   d*ˆd   d3ˆd   d!ˆd   d4ˆd   d5ˆ  d6 ˆˆd t gfƒs”J ‚ttd
 dƒttdƒ }t|ƒdt d
 g fksÊJ ‚ttƒttd
 ƒ td
t ƒ dtdƒ d  }| t|ƒd7td  d8td   d9td   d:t  d; g fƒs>J ‚| tttdƒttdƒd  d
 ƒˆd ˆ d
 ˆˆd t gfƒs†J ‚| tttdƒttdƒd  d
 ƒtd dtd   t d
 g fƒsÎJ ‚ttd< ƒd u säJ ‚| ttttt dƒ ttt dƒd  ƒˆd ˆ t ˆˆd t t gfƒs8J ‚| ttttt dƒ ttt dƒd  tƒˆd ˆ t ˆˆd t t gfƒsŽJ ‚| ttttt dƒ ttt dƒd  tƒˆd ˆd  ˆ t ˆˆd t t gfƒsìJ ‚| tttd
 dƒttd
 dƒ tddƒ ƒˆd ddtd
dƒ  ˆd   ˆd  d,dtddƒ  ˆd   d,dtddƒ  ˆd   ddtddƒ  ˆ  d ˆˆd t d
 gfƒsªJ ‚t td=d„ ƒ tttdƒttdƒ d ƒd
gksàJ ‚ttƒttd
 ƒ td
t ƒ dtdƒ d  }| t|ƒdt d d>td  d?td   d@t  dA  g fƒsTJ ‚tdBƒ‰ t|ƒˆ ksnJ ‚| tttttd
 dƒ ƒttd
 dƒ d ƒˆd ˆd  dˆ  d ˆˆd t d
 gfƒsÒJ ‚ttd d
 dƒttd d
 dƒ d }| t|ƒˆd d,ˆd   dCˆd   dDˆd   dDˆ  dE ˆˆd td  d
 gfƒsZJ ‚ttttd
 dƒ ƒttd
 dƒ d }| t|ƒˆd dˆd   d&ˆd   dˆd   dFˆd   dˆ  d ˆˆd t d
 gfƒsêJ ‚| t|dGdHˆd dIˆd   dJˆd   dKˆd   dLˆd   dMˆ  dN ˆˆd t ttd
 ƒ gfƒs^J ‚| ttttttdƒd
 ƒ ƒttdƒ d ƒˆd* dˆd   dˆd&   dˆd   ˆd  dˆd   dOˆd   dPˆ  d. ˆˆd t gfƒsúJ ‚ttttƒdƒt ttd
 dƒ d
 ƒtdQ td ttƒd   dtd  ttƒd   dt ttƒd   ttƒd   g fks‚J ‚ttdRƒƒd u s˜J ‚| ttdRƒtƒˆdt  ˆ d
 ˆˆd t t gfƒsÖJ ‚tttjt  t tƒtd
t  td  g fksJ ‚ttttƒt td  d
 tƒƒdks8J ‚ttdStd  dTtd td
dƒ  td   dUtd tddƒ  t  dt  dV td"dWƒdks J ‚tdXƒ}t|tƒdtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd  td
ƒ d tdƒt d    dtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd  td
ƒ d tdƒt d    dtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd   gksJ ‚ttd
 dƒttdƒttdƒ  }| t|ƒdˆd%  dˆd/   ˆd  d
 ˆˆdQ t gfƒs„J ‚| t|d ƒdˆd%  dˆd/   dˆd,   ˆd  d*ˆd   dˆd   d*ˆd   d*ˆd   d& ˆˆdQ t gfƒsJ ‚| tttdƒttd
 dƒd  ttd dƒ ƒˆd\ˆd  d]ˆd   d^ˆd&   ˆd  d_  ˆˆd t d
 gfƒs†J ‚| tttdƒttd
 dƒ ttd dƒd  ƒd[ˆd%  d`ˆd*   dTˆd/   dZˆd,   daˆd   dbˆd   d_ˆd&   dcˆd   ddˆd   deˆ  ˆˆd t d
 gfƒsDJ ‚| tttdƒd ttd
 dƒ ttd dƒ ƒdeˆd%  ddˆd*   d_ˆd/   dZˆd,   dcˆd   dbˆd   dTˆd&   daˆd   d`ˆd   d[ˆ  ˆˆd t d
 gfƒsJ ‚| tttdƒd ttd
 dƒ ttd dƒ d ƒdeˆd%  dfˆd*   dgˆd,   dhˆd   diˆd   djˆd&   dkˆd   dlˆd   dmˆd   dnˆd   doˆd   dpˆ  dq ˆˆd t d
 gfƒsàJ ‚tttƒttd
 ƒ td
t ƒ tdt ƒ ƒ‰ tˆ ƒd
kr8tˆ d) ƒd d… drks<J ‚tdsƒ}|dt dt  ttd td  ƒ  }|tdd&ƒ tdƒ| dI  ‰ t|td"d#}t|ƒD ]F}ttt  t|¡ t¡td"d"dt}t‡ fdudv„|D ƒƒr  qòq d sòJ ‚tttd
 ƒttdƒ d ƒtdwƒksJ ‚ttttd
 ƒƒttd
dƒ  d ƒtdxƒksRJ ‚tttƒtttƒd
 dƒ d ƒtdyƒks‚J ‚tdzƒ}| t|ƒˆˆd  tdƒˆd  t  d{dtddƒ  dtd
dƒ  ˆd   d|d*td
dƒ  ˆd   d}dtddƒ  dtddƒ  ˆd  t  d~ˆd   d~tdƒ ˆd  t  dd€td
dƒ  ˆd   d dtdƒ t    ˆˆd d‚t  tdƒtdƒtd  d„t  d… ƒ  d† gfƒsºJ ‚t|ƒg ksÌJ ‚ttdƒttdƒ ttdƒ }| t|ƒˆdQ dˆd%   dˆd/   ˆd  t ˆˆdQ t gfƒs6J ‚ttdƒttdƒ ttt dƒ }| t|ƒˆt ˆd*  dˆd/  t  dˆd,  td   ˆd td   dˆd  td   dYˆd&  td   dˆd  td   dˆd  td   dˆd  td   td   ˆˆd tt  gfƒs.J ‚t td‡d„ ƒ tttd
ƒd   ttd
ƒd   dtd
ƒd   d(tdƒd  dtd
ƒd    ƒ}| t|ƒˆd  ˆd  dtd
ƒd   d(tdƒd  dtd
ƒd    ˆˆdQ t gfƒsôJ ‚ttƒd
 ‰tˆd ˆd  ƒtd dtd   dt  d g fks>J ‚tttd
  d d tƒd u sbJ ‚ttt ƒt tttt ƒ ƒ t tttt ƒ ƒ }t|tƒtd
 gks°J ‚t|ƒd u sÂJ ‚d S )ˆNc                   S   s,   t ttƒttd ƒ tdttƒ ƒ d ƒS ©Nr|   ry   )rP   r-   ri   rt   rt   rt   ru   rœ   P  s    ztest_unrad1.<locals>.<lambda>c                   S   s*   t ttƒtd tddƒ  dttƒ  ƒS )Nr|   ry   rw   )rP   r-   ri   r   rj   rt   rt   rt   ru   rœ   R  s    rÍ   )Úclsc                    sd   t | d ƒt |d ƒksJ ‚|d r.ˆ | |ƒS | d  ¡ }|d  ¡ }||| fv ob| d |d kS ©Nr|   r   )Úboolrh  )Úrvr”   re   ra   )Ús_checkrt   ru   r¦   Y  s    
ztest_unrad1.<locals>.checkc                    sØ   t | ƒ} | d  t¡}t t|ˆ gt|ƒ ƒƒ}| d  |¡ ¡ | d d  |¡| d d  |¡gf} |d  |¡ ¡ |d d  |¡|d d  |¡gf}t| d ƒt|d ƒt|d  ƒfv oÖt| d ƒt|d ƒkS )Nr   r|   )r©   Úatomsr   Úzipr×   rÉ   rh  ri  )r­  r”   rd   Úreps©rÍ   rt   ru   r®  a  s    66&ÿztest_unrad1.<locals>.s_checkr|   ry   rw   rŽ   rx   r  r}   r¤   r6  r‡   r%  ix  iè  ià  i  rß   iÜ  iæ	  i¼  é©   r8  rý   éè   é    FrÄ   z32*sqrt(x)*(x + 1)**(1/3) + x - 4*y + (x + 1)**(2/3)r  rÆ   iúÿÿÿr˜   r   r£   r@  r‹   r¾   r'  r  c                   S   s(   t ttƒttdƒ ttd dƒ d ƒS )Nry   r|   rx   rw   )rF   r-   ri   r,   rt   rt   rt   ru   rœ   É  s    c                   S   s   t tdƒ ttƒt  ƒS r_  )rF   r-   r'   ri   rt   rt   rt   ru   rœ   Ì  r—   rù   r0  éÔ   éÀ   rG  i	=  iÈ£ im i { i  rd  c                   S   s6   t ttdƒttdƒ ttdƒ  ttd t d ¡ƒS )Nrw   ry   r‡   rx   r|   )rP   r,   ri   rÉ   rt   rt   rt   ru   rœ   æ  s    i5  iì  iÀ‰ i D z¥
        [4/5, -1484/375 + 172564/(140625*(114*sqrt(12657)/78125 +
        12459439/52734375)**(1/3)) +
        4*(114*sqrt(12657)/78125 + 12459439/52734375)**(1/3)]rú   rA  r-  r?  T)Z_reverserI  rE  é»   é  éä   r+  r  r<  rp   z!(x+y)**(2*y/3) + (x+y)**(1/3) + 1é þÿÿé@  é˜  é®  ©Z_unradz9-x + (7*y/8 - (27*x/2 + 27*sqrt(x**2)/2)**(1/3)/3)**3 - 1r*  i   iW  i   iÀ  rD  iÀ  iX  i+  iÐ  i¥  éØ   iÙ  iÚ  i@H  i¥ú iúí iÀê i Z	 iÕë2 i ` iÀÞl i@HM i©9  iÒ z0.73rp  ©r¢   r¦   c                 3   s   | ]}|ˆ    ¡ jV  qd S r   )rh  Úis_zeror[  r†  rt   ru   r–   K  r—   ztest_unrad1.<locals>.<genexpr>z_
        [(-11/(9*(47/54 + sqrt(93)/6)**(1/3)) + 1/3 + (47/54 +
        sqrt(93)/6)**(1/3))**3]a<  
        [(-sqrt(-2*(-1/16 + sqrt(6913)/16)**(1/3) + 6/(-1/16 +
        sqrt(6913)/16)**(1/3) + 17/2 + 121/(4*sqrt(-6/(-1/16 +
        sqrt(6913)/16)**(1/3) + 2*(-1/16 + sqrt(6913)/16)**(1/3) + 17/4)))/2 +
        sqrt(-6/(-1/16 + sqrt(6913)/16)**(1/3) + 2*(-1/16 +
        sqrt(6913)/16)**(1/3) + 17/4)/2 + 9/4)**3]z]
        [(-(81/2 + 3*sqrt(741)/2)**(1/3)/3 + (81/2 + 3*sqrt(741)/2)**(-1/3) +
        2)**2]a  
        -x + (1/2 - sqrt(3)*I/2)*(3*x**3/2 - x*(3*x**2 - 34)/2 + sqrt((-3*x**3
        + x*(3*x**2 - 34) + 90)**2/4 - 39304/27) - 45)**(1/3) + 34/(3*(1/2 -
        sqrt(3)*I/2)*(3*x**3/2 - x*(3*x**2 - 34)/2 + sqrt((-3*x**3 + x*(3*x**2
        - 34) + 90)**2/4 - 39304/27) - 45)**(1/3))é™   r=  éf   iT  i06  r/  i`2 i2  iìy  ix… i,ð  i*  c                   S   s&   t ttdƒttdƒ ttt dƒ ƒS )Nry   rx   )rP   r,   ri   rj   rt   rt   rt   ru   rœ   q  r—   )!r_   rƒ   r   r   rP   r-   ri   r,   r   ra   rb   rc   rj   rd   r   r±   r¡   rF   r²   r   rR   r   rl   r'   r³   r×   rv   r   ÚreversedrÉ   r   Úanyr$   )	r¦   r„   rk   rh   re   rp  r  Úxir€  rt   )r”   rÍ   r®  ru   Útest_unrad1N  s.   ÿ
ÿ"ÿÿ
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ÿÿÿÿÿ
.:
ÿ
ÿ
ÿ
ÿÿÿÿÿ
2:
ÿ
ÿ
ÿ
ÿ
ÿ
þþþþÿ

ÿ
ÿ,("

,40Fÿ*ÿ
ÿþþþý"ÿÿÿýÿ
:ÿ
"Bÿÿÿÿþþþÿ
ÿVPÿ
>$4rÈ  c                  C   s\   t dt ddtd   ƒ ƒtdt ddt ddtd   ƒ  ƒ   } t| ƒtjgksXJ ‚d S )Nr|   r‡   rw   )r-   ri   rF   r   r³   r\  rt   rt   ru   Útest_unrad_slow„  s    DrÉ  c                   C   s¬   t ttd dtd   dƒd t ƒtddƒgks6J ‚t ttd dƒttd d dƒ d ƒddttd td  dtd   dtd   dt  d d	ƒd  gks¨J ‚d S )
Nry   rw   r|   rx   r˜   r‡   rß   r‹   r   )rF   r,   ri   r   r[   rt   rt   rt   ru   Útest_unrad_failŒ  s    6&BÿrÊ  c                     s  t dƒ\‰ } }}|ˆ d  | d  }| t|ƒ tt|ƒd d ƒ ˆ t|ƒ t|ƒ tt|ƒd d ƒ i}t||ƒdks~J ‚ttˆ dƒˆ diƒdu sšJ ‚ttˆ dƒˆ diƒdu s¶J ‚ttˆ dk dƒˆ diƒdu sÖJ ‚ttˆ dk dƒˆ diƒdu söJ ‚ttˆ dk dƒˆ diƒdu sJ ‚ttˆ dk dƒˆ diƒdu s:J ‚ttˆ d ˆ d d ƒˆ diƒdu sdJ ‚tˆ d ˆ d d gˆ dƒdu sŠJ ‚tˆ d ˆ d d gˆ dƒdu s°J ‚ttˆ d d ƒˆ dƒdu sÒJ ‚tdi ƒdu sæJ ‚tdˆ d gˆ dƒdu sJ ‚tddˆ gˆ dƒdu s J ‚t| ˆ dƒdu s6J ‚tˆ d ˆ ddd	du sTJ ‚tˆ d ˆ ddd	du srJ ‚ttd
ˆ  ƒˆ ttdƒd ƒiƒdu sžJ ‚ttd
ˆ  ƒˆ ttdƒd ƒt	t
  iƒdu sÒJ ‚tdˆ d  ˆ dƒdu sðJ ‚tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nz
x, y, r, trw   r|   TFr   g»½×Ùß|Û=rd  ©Z	numericalrF  rx   re  c                      s
   t ˆ dƒS r`  ©rQ   rt   rÝ   rt   ru   rœ   ®  r—   ztest_checksol.<locals>.<lambda>c                      s   t g ˆ dƒS r`  rÌ  rt   rÝ   rt   ru   rœ   ¯  r—   )r   r-   r6   rQ   r   r   rA   r$   r%   r   r   r_   r«   )rj   rÎ   rl   r„   Zdict_var_solnrt   rÝ   ru   Útest_checksol•  s6    &ÿ  ""*&&",4rÍ  c                   C   s¢   t td ƒdtfksJ ‚t dƒdks(J ‚t tdt ƒd tƒdtdƒ tfksRJ ‚t tdt tt  ƒd tƒtd tdƒ tfksˆJ ‚t ttƒtdfksžJ ‚d S )Nrw   )rw   r   r|   ry   r   )rO   ri   r$   r%   ra   rt   rt   rt   ru   Útest__invert²  s
    *6rÎ  c                   C   sž   t t t dt ttƒ  tƒttd ƒgks2J ‚t tt ƒg ksFJ ‚t tt d ƒtttdƒƒƒgkslJ ‚t td td  td td   ƒdgksšJ ‚d S )Nrw   ry   r‡   )rF   ra   ri   r%   r$   r#   rt   rt   rt   ru   Útest_issue_4463º  s    2&rÏ  c                  C   s:  t dƒ\} }}}}}}}}}	}
}}}}}}}| |||||
|f}|||  ||  |d| d|  d|   ||  ||  |d| d|  d|	   ||  ||  |d| d|  d|   ||  |
|  |
d| d|  d|   ||  ||  |d| d|   |
|  g}tt||ddddƒdks6J ‚d S )Nza:rr|   TF)r•  r¦   r¢   )r   r×   rF   )ra   rb   rc   rd   re   r   r€   rg   rÖ   Újrf   Úlrn   rr   rì   rh   rm   rÎ   rK  r•   rt   rt   ru   Útest_issue_5114_solversÀ  s    ,****ûrÒ  c                     s  t dƒ\} }}}}}t dƒ\}}}}	}
}| | | || | || | |  | | d|  d|  d|  d|  |d  d | |	 | | d| d|  d|  |
 |d|  d|  | f	}| || |d| d|  d	|  d
|  d ||| |	|| || d d| d  |d  |||
d| d|  d|  ig‰ | ||
|||||	f‰t|gˆ¢R ddddœŽˆ kstJ ‚t|gˆ¢R dddœŽ‡fdd„ˆ D ƒks¤J ‚t|gˆ¢R ddiŽg ksÄJ ‚t|gˆ¢R Ž g ksÞJ ‚‡ fdd„|D ƒdd|| | | dddddg	ksJ ‚d S )NúI1:7údI1,dI4,dQ2,dQ4,Q2,Q4r}   rw   ry   r£   rX  rß   r‡   rŽ   rù   TF)r•  r¦   r{   ©r•  r¦   c                    s"   g | ]‰ t ‡ fd d„ˆD ƒƒ‘qS )c                    s   g | ]}ˆ   ||¡‘qS rt   )ÚgetrÕ   rè   rt   ru   Ú
<listcomp>ñ  r—   z.test_issue_5849.<locals>.<listcomp>.<listcomp>©r¨   )r‘   )Úvrè   ru   r×  ð  s   z#test_issue_5849.<locals>.<listcomp>r•  c                    s   g | ]}|  ˆ d  ¡‘qS ©r   )rÉ   )r‘   Úeir†  rt   ru   r×  ÷  s   ÿÿr   ©r   rF   ©ZI1ZI2ZI3ZI4ZI5ZI6ZdI1ZdI4ZdQ2ZdQ4ZQ2ZQ4re   rt   )r”   rÙ  ru   Útest_issue_5849Ð  s@    


*÷$ù	$ ÿ 
ÿÿrÞ  c                  C   sä   t dƒ\} }}}}}t dƒ\}}}}	}
}| | | || | || | |  | | d|  d|  d|  d|  |d  d | |	 | | d| d|  d|  |
 |d|  d|  | f	}t|| ||
|||||	ƒ	g ksàJ ‚dS )a  Same as test_issue_5849 but solved with the matrix solver.

    A solution only exists if I3 == I6 which is not generically true,
    but `solve` does not return conditions under which the solution is
    valid, only a solution that is canonical and consistent with the input.
    rÓ  rÔ  r}   rw   ry   r£   NrÜ  rÝ  rt   rt   ru   Útest_issue_5849_matrixû  s    



*÷rß  c                  C   s°  t dƒ \} }}}}}}}| |  | d| d  d| d  d| d  d|  d  | | d| d  |d  | | |d  | d| d	 d| d	  d|  d	  | | |d  d
| d  |  | | | |d	  | d  d| d |d  |  d| d d|  d|  d  | g	}| d|d|d|d|d|di| d|| |d|tdƒd |d|di| d| |d|||d|tdƒd	 |dig}	t||dd}
|
|	ks¬J |
|	fƒ‚d S )Nza, b, c, d, f, g, krx   rŽ   rw   r6  r‡   ry   r  r/  rÅ   r   r}   Trz   )r   r   rF   )ra   rb   rc   rd   r   r€   rf   ZunknownsZ	equationsZanswerÚgotrt   rt   ru   Útest_issue_21882  s"    <" ÷$&ýrá  c                     s  t tdƒ\‰ } }tdƒ}tˆ tƒtƒ}t| |ƒ|ƒ}tˆ tƒˆ tƒ t¡ ˆ tƒƒ| gks`J ‚tˆ tƒd ˆ tƒƒdgks€J ‚tˆ tƒdˆ tƒ t¡  ˆ tƒƒd| gks²J ‚tˆ tƒdˆ tƒ t¡  gˆ tƒƒˆ tƒd| iksìJ ‚tˆ tƒdˆ tƒ t¡  ˆ tƒd t d gˆ tƒtƒd| d|d  d fgksFJ ‚tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒdd||ƒ| |ƒgtˆ |ƒd | |ƒd  | ƒ ˆ |ƒ | |ƒftˆ |ƒd | |ƒd  | ƒˆ |ƒ | |ƒfhfksfJ tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒddƒ‚ˆ tƒ td¡ˆ tƒ| tƒ  d| tƒd  gˆ tƒ| tƒg}t|d	diŽd
 tdƒ tdƒftdƒtdƒ fhksàJ ‚ˆ tƒd | tƒ dˆ tƒ t¡  | tƒd d g}t|ˆ tƒ| tƒddˆ tƒ| tƒgtd| d ƒ t	dƒftd| d ƒt	dƒftd| d ƒ t	dƒ ftd| d ƒt	dƒ fhfks¨J ‚t
t‡ fdd„ƒ tˆ tƒˆ tƒ t¡ tgdˆ tƒtˆ tƒtƒ d
fksúJ ‚tˆ tƒttttfƒ tgdˆ tƒttttfƒ d
fks:J ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ d
fks‚J ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ fksÈJ ‚ttˆ tƒ|  ˆ tƒd
 |  tgdtd
| fksJ ‚tttdt tƒ ƒtdfks(J ‚tttttƒ tgdtdfksNJ ‚tttttƒ d tgdtdtd
  fks€J ‚tttttƒd  ttƒƒƒtt ƒ tt ƒhksºJ ‚ttttƒ tddttƒ gksâJ ‚tttƒttƒ tddg ksJ ‚ttttƒ tddttƒgks,J ‚ttd t d tddtd  d gks\J ‚ttd t d td ddt d gksŒJ ‚d S )NZfghra   ry   rw   r‡   r6  Tr    r¡   r|   c                      s$   t ˆ tƒˆ tƒ t¡ ˆ tƒgdS )Nr|  )rG   ri   r   rt   r^  rt   ru   rœ   U  r—   z!test_issue_5901.<locals>.<lambda>r|  r}   r   r™   )r~   r   r   r   ri   rF   r   rj   r-   r   r_   r«   rG   r;   r¡   r$   r3   r5   )r€   rg   ra   rž  ÚGr®   r•   rt   r^  ru   Útest_issue_59010  s®    ÿÿ"ÿ$ÿ8ÿ
@ÿ0.þþ@ÿü>"ÿ
6üÿ
ÿÿ
ÿ
"ÿ
"ÿ
(
ÿ
ÿ
ÿ
ÿ
ÿ

ÿ
$ÿ
ÿ

ÿrã  c                  C   sº   t ttd t d ddƒtjtdƒd  tdƒ d tj hksFJ ‚ttd t d dd} t| ƒdkr|tdd	„ | D ƒƒs€J ‚ttd t d ƒ} t| ƒdkr²td
d	„ | D ƒƒs¶J ‚d S )Nrw   çš™™™™™¹?Trš  r5  r‹   Fc                 s   s   | ]}|j V  qd S r   ©Z	is_Numberr[  rt   rt   ru   r–   x  r—   z"test_issue_5912.<locals>.<genexpr>c                 s   s   | ]}|j V  qd S r   rå  r[  rt   rt   ru   r–   z  r—   )r¡   rF   ri   r   r³   r-   r×   r§   r†  rt   rt   ru   Útest_issue_5912t  s    $ÿ"ræ  c                  C   s”  dd„ } t td ddd js"J ‚t td ddd js<J ‚t ttj ddd jsXJ ‚t td d dd jsrJ ‚t ttj d dd jsŽJ ‚| tdd	t  ƒd
dt  ƒs°J ‚ttt	fD ]D}t|dd	t  gƒƒ}t
|ƒ|u rú| t|ƒd d
dt  ƒsºJ ‚qºttd	t dd	t  giƒ ¡ ƒd \}}| |d	t ƒrR| |d d
dt  ƒsVJ ‚| ttd	t ƒƒtdt ƒƒszJ ‚| tdtd	  ƒdtd	  ƒsžJ ‚| tdtd	  dddtd  ƒsÆJ ‚| ttd	t ƒƒtdt ƒƒsêJ ‚| ttd ƒtd ƒsJ ‚| ttd d	t  ttddƒƒ d ƒtd dt  d ƒsHJ ‚dt t t }t dt | d dt | d t| d fƒg ksJ ‚d S )Nc                 S   s   t |  t¡ƒt | t¡ƒkS r   )r×   r¯  r   ©Úe1Úe2rt   rt   ru   Útest~  s    z!test_float_handling.<locals>.testrd  Trš  r   Fr|   rw   ç      ð?g       @ry   g      @rÇ   r‡   g!ÌÈ,‹ÿ?r  gffffffæ?g333333ã?gš™™™™™É?g333333Ó?rä  )rF   ri   rj  Zis_Floatr   r³   rH   r©   r¨   r¡   ÚtypeÚitemsr3   r$   r   rc   rk   rl   )rê  Zcontainr”   rf   rÙ  Ztotrt   rt   ru   Útest_float_handling}  s,    ",*,$$($&ÿ
rî  c                  C   s*   t ddd} t| d d ƒdgks&J ‚d S )Nri   Trˆ  rw   r|   rÜ  rÝ   rt   rt   ru   Útest_check_assumptions—  s    rï  c                   C   sì   t ttd ƒttd ƒ d ƒg ks(J ‚t ttd ƒttd ƒ d ƒtt tddƒ t t d tt d tt tddƒ gks†J ‚t ttd ƒttd ƒ d d ƒtt tddƒ t t d tt d tt tddƒ gksèJ ‚d S )Nry   r|   r   r‡   rw   )rF   r)   ri   r   r   r   rt   rt   rt   ru   Útest_issue_6056œ  s    (8ÿ"8ÿrð  c                  C   sV   t  ttttt ƒƒƒttt ƒƒ ƒ } t| t dƒdu s:J ‚t| t dddd u sRJ ‚d S )Nrw   TFrË  )ri   r$   r#   r%   rQ   r\  rt   rt   ru   Útest_issue_5673¤  s    &rñ  c            
      C   s¸  t dƒ\} }}}}}}}t ddd}|| | |d| | d|     |d| d|   ||  || | || | d|     ||   | | g}	t|	|| |  d||||  | d d	  ||  |  |||d	| |||  |   |||  | | d
|  |||  |   i|d|d|d|digks.J ‚t|	|||gd||||d	 |d	  t|d|  ||  ƒd	  | |d
|  t|d	 d| |  d|d	   ƒ d	| | |  ||||  | i||||d	 |d	  t|d|  ||  ƒd	  | |d
|  t|d	 d| |  d|d	   ƒ d	| | |  ||||  | ig||||d	 ||  |d	  |d	|   |||| d	  ||d	|    | ||| |d	|    igfv s´J ‚d S )Nz$R, C, Ri, Vout, V1, Vminus, Vplus, sÚRfTrˆ  r}   r|   r˜   rž   rw   ry   r   rx   rŽ   ©r   rF   r-   )
ro   rx  ZRiZVoutZV1ZVminusZVplusrÍ   rò  r•   rt   rt   ru   Útest_excludeª  sL    ÿ"(ý$(üüú,@ü,@üû$ üörô  c                  C   sV   t d dt d   dt d   tddƒ } tt| ƒƒtt| d dd ¡ ƒksRJ ‚d S )Nrx   r‡   ry   rw   rÆ   ZZZ)Údomain)ri   r   r¡   rF   rA   Z	all_rootsr²  rt   rt   ru   Útest_high_order_rootsÒ  s    *rö  c                     sÔ  dddœ} dddœ}t tt d dt t d gfi | ¤ŽtdtdiksLJ ‚t tt d dt t d gfi |¤Žtdtdiks„J ‚dd	„ }|t tt t tt t t gfi | ¤ŽƒdksÀJ ‚|t tt t tt t t gfi |¤ŽƒdksôJ ‚|t tt t tt t gfi | ¤Žƒdks&J ‚|t tt t tt t gfi |¤ŽƒdksXJ ‚tg d
¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢gƒ}ttdddƒ}tdgdgdgdgdgdgdgdgdgdgdgdggƒ}|| | }t |ƒg ksJ ‚t |ddg ks$J ‚tdd„ t tt t tt t gƒ 	¡ D ƒƒsXJ ‚dD ]d‰ tdd„ t tt t tt t gˆ dd 	¡ D ƒƒršJ ‚t
t‡ fdd „ƒ t
t‡ fd!d „ƒ q\t
td"d „ ƒ d S )#NT©ÚquickÚ
particularFrx   rw   r|   ry   c                 S   s   t dd„ |  ¡ D ƒƒS )Nc                 S   s   g | ]}|d kr|‘qS rÚ  rt   )r‘   ri   rt   rt   ru   r×  Ý  r—   z>test_minsolve_linear_system.<locals>.count.<locals>.<listcomp>)r×   Úvalues)Zdicrt   rt   ru   ÚcountÜ  s    z*test_minsolve_linear_system.<locals>.count)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   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|   )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   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˜   )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   zv:14©r  r}   r   ©rù  c                 s   s   | ]
}|V  qd S r   rt   ©r‘   rÙ  rt   rt   ru   r–   ö  r—   z.test_minsolve_linear_system.<locals>.<genexpr>)TFc                 s   s   | ]
}|V  qd S r   rt   rþ  rt   rt   ru   r–   ø  r—   c                      s   t td gˆ dS )Nr|   )rø  r   rt   ©Z_qrt   ru   rœ   ü  r—   z-test_minsolve_linear_system.<locals>.<lambda>c                      s   t td gˆ ddS )Nr|   Fr÷  r   rt   rÿ  rt   ru   rœ   ý  r—   c                   S   s   t td ddS )Nr|   Trý  r   rt   rt   rt   ru   rœ      r—   )rF   ri   rj   rk   ra   rl   r>   r   r§   rú  r_   r«   )ZpqtZpqfrû  rt  rÙ  rw  r•   rt   rÿ  ru   Útest_minsolve_linear_system×  sN    

884422ô&ÿ4
þr   c                  C   s4   t ddd} tt| d | d  d ƒƒdks0J ‚d S )Nri   Trê   rx   ry   r|   )r   r×   rF   rÝ   rt   rt   ru   Útest_real_roots  s    r  c                  C   sl   dt d  dt   dtd   d dt d  dt  t  dtd   d	 g} tt| tt d
dƒdkshJ ‚d S )NicË†rw   iQÖAiTâkl   1ö'	 iýûa5iPQRiçäžl    d(	 FrÄ   r‡   )ri   rj   r×   rF   )r•   rt   rt   ru   Útest_issue_6528	  s    "&þr  c                  C   s’   t ddd} td|  d ƒd tdd|   ƒd	 g}t|| ƒtjfgksLJ ‚t|| dd
tjfgkshJ ‚t|| dddtjftdƒfgksŽJ ‚d S )Nri   Trê   r‡   rÆ   rx   ry   rß   r|   ©r•  FrÕ  )r   r   rF   r   r³   )ri   r•   rt   rt   ru   Útest_overdetermined  s
    (r  c                  C   sÀ   t dƒ} td| d  d| d   ƒddt t tdƒ gks@J ‚t ddd} td| d  d| d   ƒdgksrJ ‚td	ƒttdƒƒ ttdƒƒ }td| d  dd|    ƒ| |gks¼J ‚d S )
Nri   r‡   rw   ry   r   Trê   rx   rŽ   )r   rF   r   r   r%   r-   )ri   rb   rt   rt   ru   Útest_issue_6605  s    8& r  c                   C   s,   t td ƒsJ ‚t tƒrJ ‚t dƒr(J ‚d S )Nrw   T)rS   ri   rt   rt   rt   ru   Útest__ispow$  s    r  c               	   C   sä   t tt d t dt  tj d  ƒ t td  d t dtd  dtd   dt  d ƒd  tddƒ d td d t t dtd  dtd   dt  d ƒd  tddƒ d  ƒ } t| tddd}t|ƒdksàJ ‚d S )Nrw   r‡   rß   r|   FrÁ  rx   )r-   rn   rm   r   r³   r   rF   r×   ©r„   r­   rt   rt   ru   Útest_issue_6644*  s*    8"ÿÿÿÿ"ÿÿÿÿÿr  c                   C   sd   t td t tt gttgƒddgks*J ‚t td tt  tt gttgƒdt t fgks`J ‚d S )Nrw   )r˜   r˜   r}  )rF   ra   rb   rc   rt   rt   rt   ru   Útest_issue_67522  s    *r	  c                   C   s¶   t ttd d  td  td t d  ƒdddttd t d dƒttd t d dƒttd t d dƒttd t d dƒttd t d dƒttd t d dƒg	ks²J ‚d S )	Nr|   rw   rŽ   r˜   r   ry   r‡   rx   )rF   ri   r[   rt   rt   rt   ru   Útest_issue_67927  s
    *.((ýr
  c                     sv  t ddd\‰ } ttˆ d ƒdtˆ d ƒ  ƒddgks<J ‚ttˆ ƒd tˆ ƒt gˆ ƒdgksdJ ‚tttˆ d	 ƒd
 ƒƒtj tdƒhksJ ‚ttt	ˆ d ƒt	ˆ d d	 ƒ dƒˆ ƒt
ddƒtdƒd  tdƒ d tj gksæJ ‚tdtˆ ƒ tˆ d ƒ ƒdt
ddƒgksJ ‚ttˆ d ˆ  d ƒˆ d  ƒg ks@J ‚ttˆ ƒƒdgksXJ ‚tttˆ d dˆ   ƒdƒˆ ƒdtdƒ dtdƒ gks–J ‚t ddd}ttt|ƒƒƒdgks¾J ‚t ddd}ttt	ddd|   ƒdƒƒt
ddƒ gksüJ ‚t dƒ‰ ttˆ ƒd tˆ ƒd gˆ ƒˆ ddt  tˆ ƒdtˆ ƒdigksJJ ‚ttˆ ƒd tˆ ƒd  ƒd }t|ƒt|ˆ ƒks‚J ‚t ddd}tt|ƒd ƒdt dt gks´J ‚tt‡ fdd„ƒ t ddd}tdˆ |  d| |   |ƒtˆ |  | d |ƒksJ ‚t ddd\‰ } tˆ | t  d ƒ| dˆ diksBJ ‚tˆ dt  ƒdgks^J ‚t ddd\‰ } tˆ | t  d dt  ƒˆ dt | dt iks¤J ‚t ddd‰ tˆ |  d dt  ƒˆ d| dt iksÞJ ‚td ƒ}t|ˆ d ƒ|dˆ  d ƒ ƒdgksJ ‚ttˆ d ƒtdˆ  d ƒ ƒdgks>J ‚t dƒ‰ tdˆ  dˆ   ƒtt tdƒ gksrJ ‚d S )!Núx yTrê   ry   rw   r|   r6  )r}   rÆ   rß   rp   r˜   r  r)  r   r‡   rx   Únn)ZnonnegativeÚnz)Únonzeror¤   ri   rÖ   ©Z	imaginaryr   c                      s   t tˆ ƒd ƒS ra  )rF   r¥  rt   rÝ   rt   ru   rœ   b  r—   zBtest_issues_6819_6820_6821_6248_8692_25777_25779.<locals>.<lambda>rz  rü  r}   r   )r   rF   r¥  r   r   r¡   r   r±   r   r   r   r-   r³   r"   r!   r   r_   rƒ   r   r%   )rj   r  r  r„   rÖ   rz  r   rt   rÝ   ru   Ú0test_issues_6819_6820_6821_6248_8692_25777_25779>  sP    ,(,&&ÿ
0*ÿ2ÿ &:&6.,,r  c                   C   s  t dtdt ƒ ttƒ tdt ƒd d  dktƒt tk ttdƒd k @ ksTJ ‚t dtdt ƒ d ttd ƒ ttƒd d  dktƒt tk ttdƒd k @ ks¬J ‚t ttƒd td  tdt d ƒ ttƒd d  dktƒt tk ttk @ ksJ ‚d S )Nrw   r   r‡   )rF   r$   ri   r   r%   rt   rt   rt   ru   Útest_issue_17638z  s    TXr  c                  C   s4  t dƒ\} }}}}}| d | | | |  | |  d ||  | |   }t dddd\}}}	|dd||    |	|    }
||
  ¡ }|t|ƒ ¡ 9 }t|| ƒ}| ¡ }|||	g}t||dd} t| ƒdksÐJ ‚|||  |||   ||| |	|| ||  i}|D ](}| d |  ¡ ||  ¡ ksJ ‚qd S )	Nzs, tau_c, tau_1, tau_2, phi, Krw   r|   zK_C, tau_I, tau_DT)r‰  r  rz   r   )r   ZtogetherrD   r¢   rA   r‚  rF   r×   )rÍ   Ztau_cZtau_1Ztau_2ÚphiÚKÚtargetZK_CZtau_IZtau_DZPIDr„   rc   ÚvarsZknownsolutionÚvarrt   rt   ru   Útest_issue_14607‚  s*    ÿ6ÿ

þr  c                     sj  ddl m‰ m‰ ttˆ dˆ   tˆ ƒ ˆ ƒˆ ƒˆ tˆ ƒhksBJ ‚tˆ ˆ ƒg ksTJ ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   ¡ƒt
dtj ƒd gks˜J ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   d d ¡ƒt
dttdƒ ƒ ƒd t
dttdƒƒ ƒd gksJ ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   ¡ƒt
dtdtdƒ ƒ ƒd t
dtdtdƒ ƒ ƒd gksnJ ‚ˆ tˆ ƒ d  ˆ ˆ tˆ ƒ ¡} t| ƒt
dtt
dƒ ƒ ƒgks´J ‚tt‡ ‡fdd„ƒ ddt
t	dƒ d ƒ t	dƒ g}tˆ d dˆ   ˆ ƒ|ks
J ‚ttdt	ˆ ƒ ˆ t	dƒ  ƒƒt|ƒks8J ‚tt
dˆ  ƒˆ ˆ ƒˆtˆƒ d gksfJ ‚d S )	Nr   ©ri   rj   r|   rw   ry   c                      s   t ˆ tˆ ƒtˆˆ  ƒ  ˆ ƒS r   )rF   r5   r%   rt   r  rt   ru   rœ   «  r—   z+test_lambert_multivariate.<locals>.<lambda>r   )rg  ri   rj   rL   rA   r$   rN   rF   rÉ   r%   r#   r   rŠ  r-   r_   rƒ   r¡   )r„   r”   rt   r  ru   Útest_lambert_multivariateŸ  s"    2D20ÿ
*6ÿ
 &" .r  c                   C   sn   t dttƒ ttdƒ  tƒdgks(J ‚tt tt tt  ƒtƒtt tttƒ t ƒ ttƒ hksjJ ‚d S ra  )rF   r5   ri   r¡   ra   r#   r%   rt   rt   rt   ru   Útest_other_lambert²  s    ( ÿr  c            
      C   sT	  t td t ttd t ƒ d ƒtddƒtddtdƒ  ƒd  tddƒtddtdƒ  ƒd  gkslJ ‚t td t ttd t d ƒ d ƒtddƒtddtdƒ  ƒd  tddƒtddtdƒ  ƒd  gksÜJ ‚t tt ttd ƒ tƒdtt d ƒ gksJ ‚t tt ttd ƒ  t¡tƒdttdƒ ttƒ d ƒ dttdƒttƒ d ƒ gkspJ ‚t dt ttd ƒ  t¡tƒdttdƒ d ƒ dttdƒd ƒ dttdƒ d dƒ gksÖJ ‚t tttƒ dt  d tƒtdttdƒ ƒ ƒgksJ ‚t td  dt  tƒdddttdƒd ƒ tdƒ gksRJ ‚t td dt  tƒdddttdƒd ƒ tdƒ gksJ ‚t dt d dd	t d   tƒ} t	| ƒdkr| d
  
¡ td	dƒtdtddƒ tdƒ d ƒdtdƒ   ksJ ‚t dt d dtddt  ƒ  tƒtddƒtdttddƒƒ d ƒd  gks\J ‚t ttƒt  ttd d ¡ƒt ttdƒ d ƒ tdtdƒ ƒgksªJ ‚tdt d  }t dt|ƒ tt|ƒ  | tƒ} dttƒ }tdƒt }td }|td| ƒ td  }|tddƒ d }| |t|| d  ƒ |t||d  ƒ |t|ƒ d gkshJ ‚ttddƒƒ}td	 }dtddƒ  }dtddƒ t }|tddƒ |tddƒ  d }t dt|ƒ | tƒ} | |td| | ƒ d |t|||  ƒ |t|||  ƒ gksJ ‚tddd}ddd| d   d|  d }	t|	|tt|	ƒ|ƒƒtddƒtdtdƒ ƒdtdƒ   gksŽJ ‚tt dttƒ ttƒd  ƒƒtdƒtdttdƒ d ƒ tdƒ ƒhksÞJ ‚t dttƒ dttƒ  ttttƒ ttƒ ƒ tƒtt tdtd  tdt ƒ ƒd  ƒt gksJJ ‚t tt ttd ƒ  td¡tƒ} t tddƒ }tdƒt }|d }| dt|d ƒ dt|| d  ƒ dt||d  ƒ gksÒJ ‚t dt ttd ƒ  td¡tƒdttddƒƒ dttddƒtdƒt d  ƒ dttddƒtdƒt d  ƒ dttddƒdƒ gks`J ‚t td td ttƒ  ttddtdtt d ƒ itdttd ƒ igks´J ‚t td td  td  tƒttdtdƒ d dttƒ d  tt tddƒ  ƒƒgksJ ‚t dtttƒd ƒd  dt  ƒttdƒ dƒd d gksXJ ‚t dtdttƒ d ƒd  t ƒttdƒ dƒd d gksœJ ‚t dttd d ƒd  td  ƒt tdttdƒƒ ƒ t tttdƒ ƒd ƒ tdttdƒ ƒ ƒtdttdƒƒ ƒtdttdƒ dƒ ƒ tdttdƒ dƒ ƒgk	sPJ ‚d S )Nrw   r|   r˜   r‡   ry   r   r}   rx   éûÿÿÿr   i ØÿÿrÆ   iëÿÿÿrŽ   rh   Trˆ  rX  rz   )rF   ri   r$   r   r-   r#   ra   r   r%   r×   rh  r,   rÉ   r   rb   r   rM   rL   rA   r¡   r3   r/   rk   rj   r   )
r”   Úaxró   rô   rL  rM  rN  rO  rh   r„   rt   rt   ru   Útest_lambert_bivariate¹  sÊ    "  þ
&  þ
48ÿ
þÿ
ÿ
@>"2ÿ
$(ÿ
$ÿ"ý ý $ÿ&ÿ4,ÿ"ý 02ÿÿ
"(ÿ
8ÿ"ÿ"ÿ"úr  c                   C   s’  t ttƒttƒ ƒdt tdt gks*J ‚t ttƒttƒ ƒdttddƒtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒt	 d  tdƒtdtdƒt	  ƒ d  ƒ gks<J ‚t ttƒttƒ ƒdt	t gksbJ ‚t dttƒ ttƒ tƒtt
jƒgksŽJ ‚d S )Nr   rw   r}   r˜   r|   ry   )rF   r5   ri   r6   r   r4   r1   r   r-   r   r   r³   r(   r)   r3   rt   rt   rt   ru   Útest_rewrite_trig  s     *@Dÿÿÿÿý&r  c                  C   sø   ddl m}  tttƒ| tƒ ƒdttddƒtdƒd  tdtdƒ d ƒd  ƒ dttddƒtdƒd  tdtdƒ d ƒd  ƒ dttdƒ d tj	 tddtdƒ  ƒd  ƒ dttddtdƒ  ƒ d tdƒd  tj	 ƒ gksôJ ‚d S )Nr   ©Úsechrw   r˜   rx   r}   )
Ú%sympy.functions.elementary.hyperbolicr   rF   r(   ri   r&   r   r-   r   r³   r  rt   rt   ru   Útest_rewrite_trigh"  s    4422ür"  c                  C   s”  t ttƒ tttdtd td     ƒ } t| tddttttt ƒ  ƒ ttttt ƒ  ƒgkshJ ‚tttd ƒtddt  ƒ d ƒdtdtdƒ ƒttddƒƒ d  tdƒd  tdtdƒ ƒ ttddƒƒ d d tdƒd  gdtd	tdƒ d
 d  ƒd  tdƒd  dtd	tdƒ d
 d  ƒd  tdƒd  gfv sTJ ‚tttdt ƒd ƒtttƒ d ƒ tdƒ ƒg ksJ ‚d S )Nr˜   rw   T)Úforcery   r|   r   iôÿÿÿiÜÿÿÿrŽ   )	rk   r%   ri   rj   rF   r-   r$   r   r)   r\  rt   rt   ru   Útest_uselogcombine-  s    ,<"02ÿ,,ÿýr$  c                   C   s.   t ttdƒtd  tƒdtdƒ gks*J ‚d S rb  )rF   r2   ri   r   r-   rt   rt   rt   ru   Ú
test_atan29  s    r%  c                   C   s„   t ttƒt tƒttƒgks J ‚t ttƒt tƒttƒgks@J ‚t ttƒt tƒttƒgks`J ‚t ttƒt tƒttƒgks€J ‚d S r   )rF   r7   ri   rj   r:   r8   r9   rt   rt   rt   ru   Útest_errorinverses=  s       r&  c               	   C   sT  t dƒ} tdƒ|  td| d  ƒ | d tdƒtd| d  ƒ d   }t|| ddd }|tddƒtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ   ddtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ     ftddƒddtd	d
ƒtdƒt d  tddƒ    td	d
ƒtdƒt d  tddƒ  fhksPJ ‚d S )Nro   rw   r|   Tr    rx   ry   r˜   éû   r¾   éo   r6  rý   )r   r-   rF   r   r   )ro   r„   r­   rt   rt   ru   Útest_issue_2725D  s,    @*ÿÿ$ÿÿÿÿÿ"ÿþr)  c                  C   sh  t dƒ\} }}}}}}}}}	}
}}}}}}t| ||  ||  g|d| d|  d|   ||  ||  g| | |d| d|  d|    ||  g| | |d| d|
  d|    |	|  g| | |	d| d|  d|    ||  g|	 | |d| d|    ggƒ}t|||	|| |gƒ}tt|ƒt|ƒdd}tdd„ | ¡ D ƒƒdksdJ ‚d S )Nzb:rr|   Fr¤  c                 s   s   | ]}|  ¡ V  qd S r   )Ú	count_ops)r‘   rÍ   rt   rt   ru   r–   \  r—   z'test_issue_5114_6611.<locals>.<genexpr>iÆ  )r   r>   rF   r©   rî   rú  )rb   rc   rd   re   r   r€   rg   rÖ   rÐ  rf   rÑ  rn   rr   rì   rh   rm   rÎ   r•   rÙ  r”   rt   rt   ru   Útest_issue_5114_6611N  s    *@\Lýr+  c                  C   sž   t ddtdƒƒ} |  ¡ t| ƒks$J ‚d| d< |  ¡ t| ƒks@J ‚t ddttdƒƒƒ} |  ¡ t| ƒkshJ ‚tdddƒ}t|ƒt|ƒ  kr”| ¡ ksšn J ‚d S )Nry   za:9r|   r}  r6  rw   )r|   rw   r|   r‡   )	r>   r   ZdetrT   r©   rð   r@   rU   rV   )rn   rÍ   rt   rt   ru   Útest_det_quick_  s    r,  c                  C   s’   t ddd\} }tt| d |d  ƒd | ƒt|d  d ƒ t|d  d ƒgksXJ ‚t ddd\} }tt| d |d  ƒd | ƒg ksŽJ ‚d S )Nza bTrê   rw   ry   r6  r  ró  rW  rt   rt   ru   Útest_real_imag_splittingk  s    $ÿr-  c                  C   sB   dt d  dt d   dt   d } tdd„ t| ƒD ƒƒs>J ‚d S )Nr}   ry   r‡   rw   rx   c                 s   s   | ]}t t |¡ƒV  qd S r   )r   r   rë   rÕ   rt   rt   ru   r–   u  r—   z"test_issue_7110.<locals>.<genexpr>)ri   rÆ  rF   rÒ   rt   rt   ru   Útest_issue_7110s  s    $r.  c                   C   s*   t dt ddt   ƒdt gks&J ‚d S r]  )rF   ri   rY   rt   rt   rt   ru   Ú
test_unitsx  s    r/  c                  C   s¢   t dƒ\} }}td|d  | |d  |  | dƒ}t|d|d  ƒ}t| d| |d  ƒ}ttt|||ƒ| ||gdƒƒ}t|ƒttd	gd
gdggƒƒksžJ ‚d S )NzA,B,Vg®Gáz²ƒ@g     €C@rú   r   g    d6 Ag    0Œ!A)r   r   r   z4442890172.68209z4289299466.1432z70.5389666628177)r   r   r>   rE   r   ri  )rt  rw  r   Úeq1Úeq2Úeq3r­   rt   rt   ru   Útest_issue_7547|  s    &
þÿr3  c                  C   s*   t ddd} tt| ƒd ƒdgks&J ‚d S )NrÎ   Trê   rw   r‡   ró  )rÎ   rt   rt   ru   Útest_issue_7895ˆ  s    r4  c                  C   sö   t ddd\} }t| d |d  ƒd t|d |  d d  ƒd  }}tddƒdtd	ƒ d  }}|| f||fg}t||f| |fƒ|ksJ ‚t||| |  f| |fƒg ks²J ‚|d
7 }t||f| |fƒg ksÔJ ‚t||f| |fdd|ksòJ ‚d S )Nr  Trê   rw   r‹   ry   é¿   rÅ   i‡  rŽ   FrÄ   )r   r-   r   rF   )ri   rj   rè  ré  ra   rb   r”   rt   rt   ru   Útest_issue_2777  s    8"r6  c                  C   s"   d} t t|  tƒd | ksJ ‚d S )Ng{[Rs±Ò8r   r   )Únumberrt   rt   ru   Útest_issue_7322›  s    r8  c                   C   s<   t tdd„ ƒ t tdd„ ƒ t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t tdddS )N)r˜   r|   Úbisect)Úmethod©rE   ri   rt   rt   rt   ru   rœ   ¡  r—   ztest_nsolve.<locals>.<lambda>c                   S   s(   t tt d tt tt ftttfdƒS )Nry   )iÎÿÿÿrû   )rE   ri   rj   rk   rt   rt   rt   ru   rœ   ¢  r—   c                   S   s   t tt tt fdƒS )Nr{  )rE   ri   rj   rt   rt   rt   ru   rœ   £  r—   c                   S   s   t tdk tdƒS )Nrd  r|   r;  rt   rt   rt   ru   rœ   ¤  r—   )r_   r«   r‚   rt   rt   rt   ru   Útest_nsolve   s    r<  c                      sæ   t tttd  t d tƒƒdks&J ‚t tttd  t d tƒƒdksLJ ‚tttd  t d tƒg ksnJ ‚ttdd„ ƒ td t d ‰ tˆ ddˆ    ƒ‡ fdd„tdƒD ƒksºJ ‚td ‰ tˆ d	dˆ    ƒtjgksâJ ‚d S )
Nry   r|   r‡   rx   c                   S   s   t ttd  t d tddS )Nrx   r|   F)Ú
incomplete)rF   ra   ri   rt   rt   rt   ru   rœ   ¬  s    z.test_high_order_multivariate.<locals>.<lambda>c                    s   g | ]}t ˆ d  |ƒ‘qS rJ  rZ   rÕ   ©rd   rt   ru   r×  ²  r—   z0test_high_order_multivariate.<locals>.<listcomp>rw   )	r×   rF   ra   ri   r_   rƒ   rð   r   r³   rt   rt   r>  ru   Útest_high_order_multivariate§  s    &&".r?  c                   C   sX   t dt d ƒdgksJ ‚t dtd  d ƒdgks8J ‚t tdddƒddgksTJ ‚d S )Nr   r|   rw   zx*(1/x**0 - x)F©Úevaluate)rF   ri   r   rt   rt   rt   ru   Útest_base_0_exp_0·  s
    ÿrB  c                   C   sd   t dtd  tgƒtƒ ksJ ‚t dtt  tgƒtt hks@J ‚t dttdƒ tgƒthks`J ‚d S )Nr|   r   ry   )rW   ri   r¡   rj   r,   rt   rt   rt   ru   Útest__simple_dens¾  s    "rC  c                   C   s”   t tttƒt td  d tƒƒdks*J ‚t tdtd  dtd tddƒ  td   dtd tddƒ  t  dt  d td	d
ƒdksJ ‚d S )Nry   r|   r»  r¼  rw   r½  r³  r¾  Fr¿  )r×   rF   r-   rj   ri   r   rt   rt   rt   ru   Útest_issue_8755Ä  s    *,ÿÿÿÿÿrD  c                  C   sP  d} d}d}d}d}d}d}d}t ttf}t |  d	 t| d	  |t d	  }	t | d	 t| d	  td	  }
t | d	 t| d	  |t d	  }|	|
|f}tt |  d	 t| d	  ƒt | }|
}tt | d	 t| d	  ƒt | }|||f}t||ƒ}t||ƒ}t||d
d}dd„ |||fD ƒ\}}}||  krF|ksLn J ‚d S )Nr   i”ýÿÿi˜  é~   r¹  r=  éÍ   éh   rw   Tr  c                 S   s   g | ]}d d„ |D ƒ‘qS )c                 S   s   h | ]}t d d„ |D ƒƒ’qS )c                 s   s   | ]}|  d ¡V  qdS )rw   N)rq   rÕ   rt   rt   ru   r–   ç  r—   z7test_issue_8828.<locals>.<listcomp>.<setcomp>.<genexpr>rØ  )r‘   rÐ  rt   rt   ru   Ú	<setcomp>ç  r—   z-test_issue_8828.<locals>.<listcomp>.<setcomp>rt   )r‘   ro   rt   rt   ru   r×  ç  r—   z#test_issue_8828.<locals>.<listcomp>)ri   rj   rk   r-   rF   )rô   Úy1Zr1rL  Úy2rM  Zy3Zr3rÙ  Úf1Úf2Zf3rp  Zg1Zg2Zg3râ  rt  rw  rx  rh   rm   rÎ   rt   rt   ru   Útest_issue_8828Í  s,    
$ $
$$


rM  c                   C   sª   t tdt ƒtdt ƒ ƒddt d dt d gks:J ‚t tdt ƒtdt ƒ ƒdt d	 td	 gksnJ ‚t dttƒ dtdt ƒ  ƒdt d td gks¦J ‚d S )
Nry   rŽ   r   r}   r6  rw   i,  rf  iÂ  )rF   r5   ri   r   rt   rt   rt   ru   Útest_issue_2840_8155ë  s    :4rN  c                   C   s"   t ddtd   ƒdgksJ ‚d S r«  r   rt   rt   rt   ru   Útest_issue_9567ó  s    rO  c                  C   s€  t tt ƒt gksJ ‚t td t ƒt ttƒ tttƒ gksFJ ‚t td dt  ƒtdt ƒ tdƒttƒ d tdƒtdƒ t ttƒ d  tdƒttƒ d tdƒtdƒ t ttƒ d  gksÒJ ‚t td tt gttƒtdtt iksüJ ‚t td d tt gttƒdt t fdt t fgks:J ‚ttd  d } tt d dt  }tt | |gttƒƒdks|J ‚d S )Nrw   ry   r‡   rX  r}   )rF   ri   r   r   r-   r+   rj   r×   rç  rt   rt   ru   Útest_issue_11538÷  s    .22ý
*ÿrP  c                  C   s€  t dƒ\} }}}}}}d| |  ||  d| |  ||  d||  ||  || d  |d  ||d  |d  ||d  |d  g}t|| ||||||gdd}t|d  d ƒ}	td|d  ƒ}
tdd|d   ƒ}tdƒ| }tdƒ|
 }|| |	 ||	 ||	 |||||di| |	||	||	|||||di| | d |
d  ||d |
d  ||
|| d |d  || d |d  |di| | d |
d  ||d |
d  ||
 || d |d  || d |d  |di| |d |
d  || d |
d  ||
|| d |d  || d |d  |di| |d |
d  || d |
d  ||
 || d |d  || d |d  |digks|J ‚d S )	Nza,b,c,d,e,f,gr|   rw   Trz   rŽ   ry   r˜   ró  )ra   rb   rc   rd   re   r   r€   Ztermsr­   rÍ   Ús2Zs3Zs4Zs5rt   rt   ru   Útest_issue_12114	  s4    66ÿ &(ÿ((ÿ&(ÿ((ÿ÷rR  c                   C   sL   t dtt  ƒg ksJ ‚t tt tƒg ks.J ‚t tt t tƒg ksHJ ‚d S r`  )rF   r   ri   rt   rt   rt   ru   Útest_inf	  s    rS  c                     sò   t dƒ‰‡fdd„tdƒD ƒ} tdƒ}tt| |ƒƒ}|d d… |dd …  \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}| d d… | dd …  \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}|| d	   |¡ ¡ ||d	   ¡ ksîJ ‚d S )
Nr   c                    s   g | ]}ˆ |ƒ‘qS rt   rt   rÕ   r^  rt   ru   r×  '	  r—   z$test_issue_12448.<locals>.<listcomp>rp   zx:15ry   c                    sT   g | ]L}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS ©r‡   r|   rw   ry   rt   rÕ   ©rc   ri   rj   rk   rt   ru   r×  ,	  s   ÿc                    sT   g | ]L}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS rT  rt   rÕ   rU  rt   ru   r×  0	  s   ÿr   )r   rð   r   r{   r°  rF   Zxreplacer*  )Zfunr˜  r±  ZssymZsfunrt   )rc   r   ri   rj   rk   ru   Útest_issue_12448%	  s&     ÿÿ ÿÿÿrV  c                   C   sî   t td dt  ƒdthks J ‚t td dt  tƒthks@J ‚t td dt  tgƒthksbJ ‚t dt dt  dt  ttgƒtthksJ ‚t dt dt  dt  ttƒtthks¼J ‚t dt dt  dt  tthƒtthksêJ ‚d S ©Nrw   r|   )rX   ri   rj   rk   rt   rt   rt   ru   Útest_denoms7	  s      ".,rX  c               &   C   s:  t dƒ\} }}}}}| d |  | | | | | | | | | | | | | | | | | | |  d |d  d| d  || |d  |d  |d  || |d  |d  |d  || d| d  |d  || | | | | || |d  |d  |d  |  d |d  |d  |d  |d  |d  | d ||  |d  |d  |d  |d  || |d  |d  |d  || | | | | || |d  |d  |d  | d ||  |d  |d  |d  |d  |  d |d  |d  |d  |d  |d  | d |d  ||  |d  | ||  | | | || d| d  |d  || |d  |d  |d  | d |d  ||  |d  |  d d| d  |d  | ||  | | | || | || | | ||  | ||  |  |d  | d g%}| d|tddƒ|tddƒ|tddƒ|tddƒ|di| d|tj|tddƒ|d|d|di| d|tddƒ|tddƒ|tddƒ|tddƒ|di| d|d|d|d|d|di| d|tddƒ|tddƒ|td	ƒd |td	ƒ d |di| d|tddƒ|tddƒ|td	ƒ d |td	ƒd |dig}t|ƒ|ks6J ‚d S )
Nzx0 x1 x2 x3 x4 x5rw   ry   rŽ   r|   r}   r˜   r   rx   )r   r   r   r³   r-   rF   )ró   rô   rL  rM  rN  rO  ro  Zsolsrt   rt   ru   Útest_issue_12476@	  s*    <DLNN20PNR>ö2"288ûrY  c                  C   s:   t dƒ} t| tdƒtdƒ  tdƒ | f| ƒg ks6J ‚d S )Nrl   rx   rw   ró  )rl   rt   rt   ru   Útest_issue_13849W	  s    rZ  c                  C   s@   ddl m} m} td| |  t t tƒd|  t gks<J ‚d S )Nr   ©ÚnewtonÚkilorß   iÀàÿÿ)Úsympy.physics.unitsr\  r]  rF   ri   rj   r[  rt   rt   ru   Útest_issue_14860\	  s    r_  c               	   C   sf  t dƒ\} }}}td|  d d |d   | d d |d   d|  d d |d   | d d |d   || d g|| ||ƒdd| td|d d  ƒ |fdd|td|d d  ƒ |fgksÊJ ‚t||| d|d   d | d d|d   d g|||ƒ|dtdƒ d f|dtdƒd fgks4J ‚t||d  d ||d  d fƒg ksbJ ‚d S )Nz:4r˜   r|   rw   r   r}   r6  ró  )rf   rg   ra   rb   rt   rt   ru   Útest_issue_14721a	  s*    ..ýý þý0ÿÿ"ÿÿ
r`  c                  C   sl   t ddd} tt| d d| d   d ƒt| d d| d   d ƒ d	t| ƒ |   | ƒtdƒgkshJ ‚d S )
Nri   Trê   r‡   é‚   rw   iA  i  rÿ   )r   rF   r-   r   rÝ   rt   rt   ru   Útest_issue_14779o	  s    0ÿÿÿÿrb  c                  C   sú   t td ttd td ddfƒtdtditdtdigks>J ‚t td tdtd ddfƒtdtdikslJ ‚t td ttd td ddfƒtdtdiksžJ ‚tdt dt  d	 d
t t ƒ} tdt d dt d ƒ}t | |gƒtdtdiksöJ ‚d S )Nrw   ry   Fr@  r   r‡   r˜   iá0  iÕW i¢éÿÿr}   rß   rý   r£   r:  )rF   rj   r
   ri   r   r   )r0  r1  rt   rt   ru   Útest_issue_15307u	  s     ÿ
ÿ 
ÿ"rc  c                   C   sÔ   t td tƒdgksJ ‚t td gtƒtdiks4J ‚t ttdtd  d  tdt  ƒtƒg ksdJ ‚t ttdtd  d  tdt  ƒgtƒg ks–J ‚t ttdtd  d  tdt  ƒttdƒgtƒg ksÐJ ‚d S )Nry   rw   r|   )rF   ri   r   rj   rt   rt   rt   ru   Útest_issue_15415	  s
    02rd  c                  C   s  t ttd dt  d td dt  d  dƒƒg d¢ks>J ‚t ttd  d ƒd	gks\J ‚t t t d  d ƒdgks~J ‚t td d
 td d  d ƒd	dgksªJ ‚t td dt  d td d  dddtdƒ    ƒtdƒgksðJ ‚t tttj  dtdƒ  ƒtdƒgksJ ‚t td d t d ƒdgksBJ ‚t tdt  d ƒddgksdJ ‚t td dt  tdƒ ƒddgksŽJ ‚t tttj  tddƒ ƒtddƒgks¼J ‚t ttdƒƒ t d ƒdtdƒtdtddƒ ƒtt	   gksJ ‚t tdƒt ttdƒƒ ƒtjgks,J ‚t tdƒ t dtdƒ  ƒddtdƒd  dt	d   dt t	 tdƒ  tdƒd dt	d    gksœJ ‚t tdƒt dtdƒ  ƒdgksÄJ ‚t tt d ƒdgksàJ ‚t dt t dt  ƒdgksJ ‚t tdƒtdƒ t dtd
ƒ d tddƒ  ƒtddƒgksHJ ‚t
dƒ} t | t | d  tƒdgksrJ ‚t | t d|   tƒdgks”J ‚t | t |  tƒdgks²J ‚t
ddd} t | t | d  tƒdgksàJ ‚t | t d|   tƒdgksJ ‚d S )Nrw   rÆ   r  r  rš   r|   )rw   ry   r‡   rx   rŽ   rÆ   r‡   r}   rŽ   ry   r%  rß   r6  rx   rb   r˜   Trˆ  )rF   r   ri   r-   r   r³   r   r%   r   r   r   )rb   rt   rt   ru   Útest_issue_15731‰	  s4    >",F.$"*.F*Fÿ($D"""re  c                   C   sJ   t td ttd   tƒsJ ‚t ttd  td  td  d ƒsFJ ‚d S )Nr‡   rä  ry   rw   rë  )rF   ri   rj   r   rt   rt   rt   ru   Útest_issue_10933©	  s    rf  c                  C   s,   t ddd} tt| t ƒ| ƒdgks(J ‚d S )Nri   Trê   r   )r   rF   r¥  rj   rÝ   rt   rt   ru   Útest_Abs_handling®	  s    rg  c                  C   s†   t dƒ} td| d  d|   d dk| dkg| ƒtju s<J ‚t| d d| d   d	|  d  d
 dk| d dkg| gƒtju s‚J ‚d S )Nri   rw   rx   rÅ   r   g      ø?ry   g)\Âõ( @g=
×£p=L@éj   r|   )r   rF   r   ÚfalserÝ   rt   rt   ru   Útest_issue_7982³	  s    4rj  c                  C   sP   t dƒ\} }t| | |  | | | |  | g| |gƒ||d  |fgksLJ ‚d S )Nr  r|   rÜ  r  rt   rt   ru   Útest_issue_14645»	  s    rk  c                  C   sR   t dƒ\} }ttd| dk f| | dkfƒ| ƒ|td| dk f| dfƒigksNJ ‚d S )Nr  r¥   rä  T)r   rF   r.   r  rt   rt   ru   Útest_issue_12024À	  s     ÿrl  c                   C   s¬   t dt t t tƒtttƒtt  ƒ ttdƒƒ tttƒtt  ƒttdƒƒ gks\J ‚t ttd  td  tƒttdtdƒ dttƒ  dt t  ƒƒgks¨J ‚d S )NrÆ   r  iõÿÿÿ)rF   ri   r   r-   r%   r   r$   r#   rt   rt   rt   ru   Útest_issue_17452Æ	  s    4ÿ
rm  c                   C   s0   t tttdƒd  ƒt  t tƒg ks,J ‚d S r©  )rF   r7   ri   r   r   r   rt   rt   rt   ru   Útest_issue_17799Ì	  s    rn  c                  C   sN   t ddd} ttt| d d ƒ|  ƒ|  ƒddtdƒ dtdƒ gksJJ ‚d S )Nri   Trê   rw   r|   r˜   )r   rF   r¥  r-   rÝ   rt   rt   ru   Útest_issue_17650Ð	  s    ro  c                  C   s\   dt d  dt d d tdƒd    ddt d d tdƒd     } t| ƒd u sXJ ‚d S )Néøÿÿÿrw   r6  r|   r‡   ry   )ri   r   rP   r\  rt   rt   ru   Útest_issue_17882Õ	  s    Hrq  c                   C   s„   t tt
 td  ƒtƒg ks J ‚t tt td  ƒtƒg ks@J ‚t tt
 td  ƒtƒg ks`J ‚t tt td  ƒtƒg ks€J ‚d S r_  )rF   r$   ri   rt   rt   rt   ru   Útest_issue_17949Ú	  s       rr  c                   C   s  t tttdƒdƒƒddgks J ‚t tttdƒttdƒ tƒƒg d¢ksJJ ‚t tttdƒdƒƒddgksjJ ‚t tttdƒ tƒttdƒ gksJ ‚t tttdƒ ttdƒ ttƒ tƒttƒ ttdƒ ttdƒ gksÚJ ‚t td ttd dƒ tƒg d¢ksJ ‚d S )Nrw   ry   r}   )rX  r   r|   r   r|   )r}   r˜   ry   )rF   r   r   ri   Úpowra   rj   r5   rt   rt   rt   ru   Útest_issue_10993á	  s     * &Jrt  c                  C   sr   t t d } t t }t| |gt tƒt t tdt iks:J ‚t d t }t| |gt tƒt dt tdt iksnJ ‚d S )Nr|   r˜   rw   r}   )ri   rj   r   rF   r   )r0  r1  r2  rt   rt   ru   Útest_issue_11553ê	  s
    &ru  c                  C   sÀ  t dƒd } tttƒd ttƒd  ƒ tdttƒd  dttƒd   ƒtd|  ƒtd|  dtdƒt   d ƒ td|  dtdƒt   d ƒ gksžJ ‚t j}tttƒd ttƒ ƒdt| tdƒd  tdƒtdtdƒ ƒ d  ƒ dt|tdƒd  tdƒtdtdƒ ƒ d  ƒ dttdƒ d | tdƒtdtdƒ ƒ d  ƒ dttdƒ tdtdƒ ƒ d | tdƒd  ƒ gks”J ‚tdttƒ ttƒ ƒtdƒgks¼J ‚d S )Nr|   ry   rx   r‡   rw   r}   )	r   rF   r3   ri   r5   r1   r-   r   r³   )rl   rg   rt   rt   ru   Útest_issue_19113_19102ò	  s    "* þ
4244ürv  c               	   C   sª   t dƒd } t dƒd }tdƒd }tdƒd }tdtd d  d ƒd| |  t| | ƒ | |  t| | ƒ ||  t| | ƒ ||  t| | ƒ gks¦J ‚d S )Nry   r‡   rx   rß   r|   rw   )r   r-   rF   ri   ©ra   rb   rc   rd   rt   rt   ru   Útest_issue_19509
  s    ürx  c               	   C   sò   t dƒ\	} }}}}}}}}|| | |  | }	d|d | d  | dt||	 ƒ   }
||||	t|
ƒ    }dt|| | ||| | |  |   ƒ dt||| | |  |  ƒ  }| |d|   |d|   d g}t||ƒ|ksîJ ‚d S )NzTHT HT DBH dib c0 c1 c2 c3 c4r|   )r   r$   r%   rF   )ZTHTZHTZDBHZdibZc0Zc1Úc2Úc3Zc4r   Úrhsr„   Ztermr­   rt   rt   ru   Útest_issue_20747
  s    (*ÿ"r|  c            	   	   C   s   t ttd ftttfddtdigks*J ‚tdƒ } \}}}}}d|d  | d|d  |d   d|d  | |  |d	 d  d|d  |  d| |d   d| |d   d| |  d
|d  d|d  |d   d|d  |  d|d  d  d|d  |  d|d   |d  d|  d|d  d| |d   d| |  d|d  | d|d   d| |  g}|d|d  |d d  ||d  i|d|d||d  |d d  ig}t || dd|ksØJ ‚t t|| ƒdd }|ksüJ |ƒ‚d S )Nrw   Trz   r   za1:6rß   r‡   ry   rx   r£   rŽ   r¤   rp  )rF   ri   rj   rk   r   rB   )	rÍ   Za1Za2Úa3Za4Za5r•   r­   r€   rt   rt   ru   Útest_issue_27001
  s@    *Rÿÿ
ÿÿÿÿ
ÿÿÿ
ÿ
ÿ&ýHr~  c                  C   s2  t dt  d  } t|  t dt d i¡ t¡dktƒtdƒtk ttdƒd k @ ksVJ ‚t|  t dt d i¡ t¡dktƒtdƒd tk ttdƒd k @ ks J ‚t|  t dt d i¡ t¡dktƒtd	ƒd tk ttdƒk @ ksæJ ‚t|  t dt d i¡ t¡dktƒtdƒtk ttdƒd k @ ks.J ‚d S )
Nr|   rw   ry   r   r˜   rX  r}   r‡   r  )rl   rF   rÉ   ri   r   r   r^  rt   rt   ru   Útest_issue_20902#
  s
    FJFr  c                  C   sÀ   t ddd} tttdƒƒ ttt| ƒƒ tttƒ g}t|tttƒttdƒƒtt| ƒƒtttdƒƒƒfgkspJ ‚t	tƒt	t ƒ ttƒt	tƒt	t ƒ   t d g}t|tƒtdiks¼J ‚d S )Nra   Trê   r‡   rx   )
r   ri   r'   r3   rj   r(   rk   r)   rF   r$   )ra   r„  Z	newsystemrt   rt   ru   Útest_issue_21034+
  s
    *:6r€  c                  C   sÔ   t ttd t d  td td   td  ƒ t d td   } tt t d td   }t||   t t   ||  ft||   t t   ||  fg}ttd td  td  t t tt  t gttƒ|ksÐJ ‚d S r_  )ra   r-   ro   rb   rc   rF   ri   rj   )rk   rl   r­   rt   rt   ru   Útest_issue_48866
  s    @<r  c                  C   sT   t ddd\} }}}t| |t  ||t   tƒt||  ƒt|| ƒ gksPJ ‚d S )Nrs  Trˆ  )r   rF   ri   r%   rw  rt   rt   ru   Útest_issue_6819=
  s    r‚  c                  C   s0   t dƒ} td|  t d | ƒdt gks,J ‚d S )Nri   r|   r‡   )r   rF   r   rÝ   rt   rt   ru   Útest_issue_17454B
  s    rƒ  c                  C   sB   ddt dƒ d  g} tdt t dtd  ƒ d ƒ| ks>J ‚d S )Nr*  rw   )r-   rF   ri   )r»   rt   rt   ru   Útest_issue_21852G
  s    r„  c                  C   sŒ   t  ttdt   tdt  dt   ddt    } t| tddd}|ttdt   tdt   t dt   t ddt   gksˆJ ‚d S )Nr|   FrÁ  )rd   ra   rc   re   rb   rF   r  rt   rt   ru   Útest_issue_21942L
  s    6
ÿÿ
ÿr…  c                  C   sP   t td td  t d dd} t td td  t d dd}| |ksLJ ‚d S )Nrx   rw   r|   F)ZcubicsTr   )r,   Zradrt   rt   ru   Útest_solver_flagsS
  s      r†  c                  C   s’   dt d  dtd d  td   } t|  ¡ t dddt td d  tdtdƒt   td d  t dtdƒt   td d  gksŽJ ‚d S )	Nrw   ry   r¤   r|   rŽ   Fr¤  r˜   )ri   rj   rk   rF   rh  r-   r   r\  rt   rt   ru   Útest_issue_22768Y
  s    $0 ÿÿr‡  c                   C   sZ   t td  ttd t ƒ d dt t dt t  fƒtdttitdttigksVJ ‚d S )Nrw   r}   r˜   r|   )rF   rj   r%   ri   r   rt   rt   rt   ru   Útest_issue_22717`
  s    8ÿrˆ  c                     s6   t d d d ‰ tˆ ƒ} t‡ fdd„| D ƒƒr2J ‚d S )Nrx   rp  ry   c                 3   s   | ]}ˆ   t|¡V  qd S r   )rÉ   ri   rÕ   r\  rt   ru   r–   h
  r—   z#test_issue_25176.<locals>.<genexpr>)ri   rF   rÆ  rØ   rt   r\  ru   Útest_issue_25176e
  s    r‰  c                  C   s²  t dt td tt t t   td dt dtddƒ t  dt  t dtddƒ t  dt  t   td ddtddƒ  t t	dƒt  dtddƒ t  dt  t	dƒt  ddtddƒ  t  dtddƒ t  dt    td dt	dƒ t ddtddƒ  t  t	dƒt  dt	dƒ t  t	dƒt  ddtddƒ  t    tdt dt  dt	dƒ t  dt	dƒ t    d ƒ} t
| ttttttgtƒttddƒttdd	ƒttd
dƒddtddƒ  d  ddtddƒ  d	  tddtddƒ  d dt	dƒ d  ddtddƒ  d  ttd
dƒddtddƒ  d	  ddtddƒ  d  tdt	dƒ d ddtddƒ  d  ddtddƒ  d  iks®J ‚d S )Nrp  rx   r‡   rw   ry   rX  rß   r  i  iØÿÿÿé   r|   iìÿÿÿr‹   i  iöÿÿÿrÅ   )r   ra   ri   rb   rc   re   r   rd   rf   r-   rK   r\  rt   rt   ru   Útest_issue_10169k
  sV    Fÿÿÿÿ&ÿÿ
ÿÿÿÿÿF
ÿÿý ÿüû

6<6<úr‹  c                  C   sB  t dƒ\} }}}t| ttƒ |ttƒ  |tt| ƒ ƒ}|j|j jdd}t|||ftƒ}||dt	| t
| d |d  ƒ | ƒ || d  | t
| d |d  ƒ  |d  | t
| d |d  ƒ  i|dt	| t
| d |d  ƒ | ƒ || d | t
| d |d  ƒ  |d  | t
| d |d  ƒ  d igks>J ‚d S )NzA, B, r, phiT)Ztrigrw   r˜   )r   r   r5   rl   r3   Úlhsr{  rh  rK   r1   r-   )rt  rw  rÎ   r  re   r„   rn  rt   rt   ru   Ú*test_solve_undetermined_coeffs_issue_23927|
  s    *$Bþ$Dþýr  c                      sL   t tdd„ ƒ tdddd‰tˆd tdƒd  ƒ‰ t t‡ ‡fdd„ƒ d S )	Nc                   S   s   t ttd dƒtƒS )Nrw   r@  )rF   r	   ri   rt   rt   rt   ru   rœ   Œ
  r—   z"test_issue_24368.<locals>.<lambda>rQ  TrŒ  rw   r|   c                      sn   t tˆ d ˆ d  dˆ  ˆ d   dˆ d   dƒˆ  tˆ d ˆ d  dˆ  ˆ d   dˆ d   dƒ ˆƒS rW  )rF   r	   rt   ©r   rQ  rt   ru   rœ   
  r—   )r_   rƒ   r   r*   r   rt   rt   rŽ  ru   Útest_issue_24368‰
  s    r  c                   C   sî  t dƒd gtdtt jtdkfdt dtd d  d  d tdktdk@ tdk@ tdk@ tdk @ fd	d
t  tdktdk@ tdk@ tdk @ fdt dtd d  d  d tdktdk@ tdk@ tdk @ fd	dt  tdktdk@ tdk @ fdt dtd d  d  d tdktdk@ tdk@ tdk @ fddt  tdktdk@ tdk @ fd
t dtd d  d  d tdktdk@ tdk @ fddt  tdktdk @ fdt dtd d  d  d tdktdk@ tdk@ tdk @ fddt  tdktdk@ tdk @ fdt dtd d  d  d tdktdk@ tdk @ fddt  tdktdk @ fdt dtd d  d  d tdktdk@ tdk @ fdt tdktdk @ fdt dtd d  d  d tdktdk @ fdtdk ft jdfƒ ƒksêJ ‚d S )Nr‹   ry   r   rÅ   rŽ   rw   é°   r‡   r  r?  r¤   r-  éÄ   rA  rý   é   r  rû   r¹  r&  T)r   rF   r.   ÚNaNri   rt   rt   rt   ru   Útest_solve_Piecewise’
  s(    F*>">"6>"66.
îr”  N)rp   ()  Zsympy.assumptions.askr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.functionr   r   r   Zsympy.core.modr	   Zsympy.core.mulr
   Z
sympy.corer   r   Zsympy.core.numbersr   r   r   r   r   r   Zsympy.core.relationalr   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   r   r   Zsympy.core.sympifyr   Z(sympy.functions.combinatorial.factorialsr   Z$sympy.functions.elementary.complexesr   r   r    r!   r"   Z&sympy.functions.elementary.exponentialr#   r$   r%   r!  r&   r'   r(   r)   Z#sympy.functions.elementary.integersr*   Z(sympy.functions.elementary.miscellaneousr+   r,   r-   Z$sympy.functions.elementary.piecewiser.   Z(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Z'sympy.functions.special.error_functionsr7   r8   r9   r:   Zsympy.integrals.integralsr;   Zsympy.logic.boolalgr<   r=   Zsympy.matrices.denser>   Zsympy.matricesr?   r@   Zsympy.polys.polytoolsrA   rB   Zsympy.printing.strrC   Zsympy.simplify.radsimprD   Zsympy.solvers.solversrE   rF   rG   rH   Zsympy.solversrI   rJ   rK   Zsympy.solvers.bivariaterL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   r^  rY   Zsympy.polys.rootoftoolsr[   Zsympy.testing.pytestr\   r]   r^   r_   Zsympy.core.randomr`   rÊ   rg  ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rv   r   r†   rˆ   r‰   rŠ   rŒ   r¯   r¼   r½   r¿   rÀ   rÁ   rÐ   rÑ   rÓ   rÙ   rÚ   rÛ   rÜ   rÞ   rà   rá   râ   rã   rå   rç   ré   r÷   rU  rV  rm  rq  rr  ry  r~  rƒ  r…  r‡  r‹  rŽ  r  r  r‘  r™  r›  rœ  r£  r¦  r§  r¨  rÈ  rÉ  rÊ  rÍ  rÎ  rÏ  rÒ  rÞ  rß  rá  rã  ræ  rî  rï  rð  rñ  rô  rö  r   r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r"  r$  r%  r&  r)  r+  r,  r-  r.  r/  r3  r4  r6  r8  r<  r?  rB  rC  rD  rM  rN  rO  rP  rR  rS  rV  rX  rY  rZ  r_  r`  rb  rc  rd  re  rf  rg  rj  rk  rl  rm  rn  ro  rq  rr  rt  ru  rv  rx  r|  r~  r  r€  r  r‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  r‹  r  r  r”  rt   rt   rt   ru   Ú<module>   sœ   (0D
h$


7
 3('-
,



  7


+D	(,	
<

[



	

			