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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   úO/var/www/auris/lib/python3.10/site-packages/sympy/solvers/tests/test_solvers.pyÚNS/   ó   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sFJ ‚t||d t  t ||gdd|t|digks`J ‚t| dƒd td gddtd	| dƒdigksyJ ‚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    ÿ046r‚   c              	   C   s*   zt | |ƒ W dS  ttfy   Y dS w )NTF)rF   Ú	TypeErrorÚNotImplementedError)ÚeqÚsymbolrt   rt   ru   Úguess_solve_strategy=   s   
ÿr‡   c                   C   s  t tdƒtƒs	J ‚t ttƒsJ ‚t tt tƒsJ ‚t dt tƒs"J ‚t ttdƒ tƒs-J ‚t tdtddƒ  tƒs;J ‚t td d tƒsFJ ‚t td d tƒsQJ ‚t tt t tƒs\J ‚t tttƒ t tƒsiJ ‚t ttd  td tdtd  ƒ  tƒs€J ‚d S )Né   rx   r}   rz   )r‡   r   ri   ra   r-   r   rj   r$   rt   rt   rt   ru   Útest_guess_polyE   s   $ÿr‰   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s,J ‚t tdt  t tƒs9J ‚d S )Nr}   rz   rˆ   )r‡   r-   ri   r   rj   rt   rt   rt   ru   Útest_guess_poly_cvU   s   ÿrŠ   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s&J ‚t ttƒd ttddƒ ttƒ d  tƒs>J ‚d S )Nr}   rx   rz   )r‡   ri   rj   r-   r   rt   rt   rt   ru   Útest_guess_rational_cv`   s
   $ÿ4r‹   c                   C   sœ   t ttƒd tƒsJ ‚t dttƒ t tƒsJ ‚t ttƒtt ƒ t tƒs(J ‚t dt d tƒs3J ‚t dt  d tƒs?J ‚t ttt  t tƒsLJ ‚d S )Nr}   rx   rz   é
   )r‡   r$   ri   r3   rj   ra   rb   rt   rt   rt   ru   Útest_guess_transcendentalk   s   ÿr   c               	      sF	  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s*J ‚ttˆŽ t tƒˆ ks6J ‚ttt d d	 ƒƒt	dƒt	dƒ hksKJ ‚tt t d
 t t d gƒt d	tdiksaJ ‚tt t
t ƒ t ddt
t ƒgkssJ ‚tdƒtdt ƒ  krƒg ks†J ‚ J ‚tddgƒg ksJ ‚ttdƒgt gƒg ksJ ‚ttdd„ ƒ ttdd„ ƒ tt t ttgddgks¹J ‚ttdd„ ƒ ttdd„ ƒ tt t ttgddgksÕJ ‚ttd
 thƒd
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igksòJ ‚tt t d
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t tfgksJ ‚tt t d
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t igksJ ‚tt t d
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t igks0J ‚tttt   d ttgƒtdtdiksFJ ‚ttt t  t t ttgƒtt ttiks_J ‚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sªJ ‚t| tttgdd|gksºJ ‚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sçJ ‚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sJ ‚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ƒt fƒt tdƒ ttdƒ igksÊJ ‚ttt
t ƒt  gt tƒtdƒ dfgksáJ ‚tt d t tƒt d gksòJ ‚tg t gƒg ksýJ ‚tt d d	 td ft tƒddgksJ ‚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s_J ‚tt t d d	 t t d gƒt t d igkszJ ‚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s¥J ‚tdtt dƒgt gddt digksºJ ‚ttt t ƒtt dƒtt t d ƒgt gddg ksÕJ ‚ttt t d ƒt dk gt ƒræJ ‚ttt dƒt d dk gƒtt dƒksûJ ‚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s-J ‚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sZJ ‚tttd t td
ƒt  fƒ ¡ ƒt tgkssJ ‚tt d t gtt fddtt gtƒ fksŠJ ‚tt d t gtt hddt tgtƒ fks¡J ‚d S )"Néýÿÿÿr}   ry   rx   é   rp   c                 3   s$    | ]}t |ˆƒttƒˆ kV  qd S ©N©rF   ri   rj   )Ú.0Ú	container©ÚansÚeqsrt   ru   Ú	<genexpr>{   s   €" z"test_solve_args.<locals>.<genexpr>rˆ   rz   éÿÿÿÿT©Zimplicité*   c                   S   ó   t td td ftttƒS ©Nrz   rx   r‘   rt   rt   rt   ru   Ú<lambda>‡   ó    z!test_solve_args.<locals>.<lambda>c                   S   ó   t tttƒS r   ©rF   ri   rt   rt   rt   ru   r   ˆ   ó    ©Úexcluder   c                   S   r›   rœ   r‘   rt   rt   rt   ru   r   Œ   rž   c                   S   rŸ   r   r    rt   rt   rt   ru   r      r¡   r{   ©ÚsetF)r£   Úsimplifyé   é   c                   S   s$   t ttƒttƒ ttƒ ttƒ ƒS r   )rF   r$   ri   r5   rj   rt   rt   rt   ru   r   ³   ó   $ )r~   rx   )rx   rx   )rx   r~   ç        )r¥   Úcheck)ri   rj   ÚallÚtupleÚlistr¥   Ú	frozensetrF   r   r   r$   r-   r_   Ú
ValueErrorra   rb   rc   rg   rh   rf   r„   r#   r   rk   r   Úkeys)r…   ÚsolÚargsrt   r”   ru   Útest_solve_argsw   sž   $
ÿ*,$& *.$,28D >
ÿ8
ÿ,2F
ÿ&ÿ.ÿ
ÿ."***
þ
ÿ68*6"*((.ÿ
ÿ2.2r´   c                  C   sÆ  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s#J ‚tt td d tƒƒtj tjhks7J ‚tt ttd dƒtƒƒtj tjhksLJ ‚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sÑJ ‚ttjttji}t tt tt fttƒ|kséJ ‚t tt tt fttfƒ|ksúJ ‚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s/J ‚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saJ ‚d S )Nrz   rx   r}   úa11,a12,a21,a22,b1,b2rp   rˆ   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ÿrÁ   c                   C   s   t dtƒg ks	J ‚d S )Nrˆ   r    rt   rt   rt   ru   Útest_solve_polynomial2  ó   rÂ   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sJ ‚t ttddƒ d tƒdgks-J ‚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sXJ ‚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}   rx   rˆ   r¨   rz   é   r   N)rF   r-   ri   r   rt   rt   rt   ru   Útest_solve_polynomial_cv_1a  s
   ""8rÅ   c                   C   sj   t tdt dtttƒ   tƒƒtjdtd  hksJ ‚t ttttdƒd  tƒƒtjtdƒhks3J ‚d S )Nrˆ   r}   rx   rz   rÄ   )r¥   rF   ri   ra   r-   r   r·   r,   rt   rt   rt   ru   Útest_solve_polynomial_cv_1b  s   82rÆ   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 s9J ‚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}   rz   rx   N)rF   ri   r   r¸   r   r-   rt   rt   rt   ru   Útest_solve_polynomial_cv_2  s
   **ÿÿrÇ   c                  C   s  t d dt d   dt d   dt   d } t| dd	}|D ]}|  t | ¡ ¡ ¡ }t|d
ƒs1J ‚qt d dt d   dt d   dt   d } t| ƒ}|D ]	}|jtksWJ ‚qNttt d dt d   d ƒd
 ddtt d dt d   d d
ƒ ¡ ksJ ‚d S )Nry   én   rz   é7   rx   i	  iÓ  F©r«   r   rp   rŒ   é   é   ©Úexponent)ri   rF   Úsubsrr   ÚtnÚfuncr[   rH   ©r€   ÚsÚrÚresrt   rt   ru   Útest_quintics_1"  s   ,,&	 ÿrÖ   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sKJ ‚qBt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sÔJ ‚d S )Nry   rp   r§   FrÊ   r   rz   rx   rŒ   rË   r   r}   rˆ   )ri   rF   rÏ   rr   rÐ   rÑ   r[   rÒ   rt   rt   ru   Útest_quintics_29  s    ,*,,,,,ûr×   c                  C   sH   t d t d  dtddƒ  } t| ƒt|  ƒ  krg ks"J ‚ J ‚d S )Nry   rz   rx   r}   )ri   r   rF   ©rj   rt   rt   ru   Útest_quintics_3L  s   *rÙ   c                  C   s>   t td dt  d ƒ} tdd„ | D ƒƒrt| ƒdksJ ‚d S )Nr   rx   c                 s   s    | ]}t |tƒV  qd S r   )Ú
isinstancer[   ©r’   Úirt   rt   ru   r—   T  ó   € z&test_highorder_poly.<locals>.<genexpr>)rF   ri   r¬   Úlen©r²   rt   rt   ru   Útest_highorder_polyQ  s   &rà   c                   C   s<   t ttd  td tdtd  ƒ  tƒtd gksJ ‚dS )z!Test solve for rational functionsrz   rx   r}   N)rF   ri   rj   r-   rt   rt   rt   ru   Útest_solve_rationalW  s   <rá   c                   C   s&   t ttƒd t ƒdt gksJ ‚dS )z)Test solve for simple conjugate functionsrz   N)rF   r    ri   r   rt   rt   rt   ru   Útest_solve_conjugate\  s   &râ   c                   C   sˆ   t td td  ttddtt ittigksJ ‚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sBJ ‚d S )Nrx   Tr{   )rF   ri   rj   r$   r-   rt   rt   rt   ru   Útest_solve_nonlineara  s   26ÿrã   c                  C   sl   t dƒ} tt| d d| d d   dd| d d   ƒ| ƒg ks"J ‚tt| d|   d|  ƒ| ƒg ks4J ‚d S )Nri   rx   r}   rˆ   )r   rF   r   ©ri   rt   rt   ru   Útest_issue_8666g  s   <(rå   c                   C   s:   t ddtd  dt   d tƒtddƒtjgksJ ‚d S )Nrˆ   rx   é   rŽ   )rF   ri   r   r   r¸   rt   rt   rt   ru   Útest_issue_7228m  s   :rç   c                   C   s0   t ttd ƒttd ƒ tƒtdƒgksJ ‚d S )Nrz   rŒ   )rF   r%   ri   r-   rt   rt   rt   ru   Útest_issue_7190q  ó   0rè   c                  C   s<   t dƒ} | t| d d ƒ }| | ¡}t|| ƒg ksJ ‚d S )Nri   rx   r}   )r   r-   r   rF   )ri   r€   Zf_diffrt   rt   ru   Útest_issue_21004u  s   
rê   c                  C   st   t dƒ} ttt| t| dƒ| dkB fƒdƒƒ}|dgksJ ‚ttt| t| dƒ| dkB fƒdƒ| dd}|du s8J ‚d S )Nri   r   r}   rß   T)r   rF   r   r.   rQ   )ri   rÔ   rt   rt   ru   Útest_issue_24650|  s
   $*rë   c               	   C   s®  t dƒ\} }}}}t| d | | | d|  |d g| |gƒg ks"J ‚t| d | | | d|  | d g| |gƒg ks;J ‚t| d | d | | | d|  g| |gƒg ksTJ ‚t| d|  d d|  d|  d g| |ƒ| d|diksrJ ‚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s¸J ‚t| | | | | | g| |||ƒ| | || iksÕJ ‚d S )Nzx, y, z, t, nr}   rx   ry   rŽ   r   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>rí   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s!J ‚d S )N)r   g      .@ç      $@g     à…@)r}   r}   r}   g      Y@)r   rî   g      @g      i@)g      Àr   r   r   r   g      NÀg      d@)r>   rI   ri   rj   rk   )rì   rt   rt   ru   Útest_linear_system_xfail˜  s   ý&rï   c                  C   sš   t dƒ} t| ddƒ| ddƒ | ddƒ | ddƒ | ddƒ | ddƒ g| ddƒ| ddƒ| ddƒ| ddƒƒ| ddƒ| ddƒ | ddƒ| ddƒ iksKJ ‚d S )Nra   r   r}   )r   rF   ©ra   rt   rt   ru   Útest_linear_system_function£  s   > ÿ&ÿrñ   c                  C   s2   dd„ } t ddƒD ]}| |ƒ\}}t||ƒ q	d S )Nc           
         sÔ   d|  d }t ddd\‰ }}t d | ¡dd}t d | ¡dd}t d |d ¡dd}t‡ fd	d
„t|ƒD ƒƒ}g }t| ƒD ]&}	| | ˆ |	¡ ˆ |i¡||	  ¡ | | ˆ |	¡ ˆ |i¡||	  ¡ q?||fS )Nrx   r}   z	x, x0, x1T©Úrealzy0_:{}zy1_:{}zc_:{}c                 3   s     | ]\}}|ˆ |  V  qd S r   rt   )r’   ÚoZcoeffrä   rt   ru   r—   ´  s   € zLtest_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqs.<locals>.<genexpr>)r   ÚformatÚsumÚ	enumerateÚrangeÚappendr   rÏ   )
ZwyÚorderÚx0Úx1Zy0sZy1src   Úexprr–   rÜ   rt   rä   ru   Ú_mk_eqs«  s   $&z9test_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqsr}   ræ   )rø   rF   )rþ   rr   r–   rc   rt   rt   ru   Ú(test_linear_system_symbols_doesnt_hang_1©  s
   þrÿ   c                  C   s0  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 }\}}}}}}}}	}
}}}}}}}}}}i |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$ƒd “|td%ƒ d “|td&ƒ d “|td'ƒ d( “|td)ƒd( “|td*ƒ d “|td+ƒd, “|td-ƒ d “|td.ƒd  “|td/ƒ d |td0ƒd i¥}t| t |d1 ƒ ƒ}t||ƒ|ksüJ ‚td2ƒ}t||  t |d1 ƒ ƒ}t||ƒ|ksJ ‚d S )3N)éB   é   é'   é2   éX   é(   é%   é`   r¨   éA   é   é   r  éH   r¨   é   rÉ   r  é   éL   )rŒ   é]   é"   éb   é;   é,   éC   éJ   r  é^   éG   é=   é<   é   r   rx   é9   ræ   é   éN   )r  é[   r  é   é@   r  r  é5   éM   r  éU   é:   éW   r  r  rÌ   é$   r  r  rz   )r  éF   rp   r!  éD   é+   éV   éS   éQ   r  é   é.   r  é   r  r-  r  r  é?   r   )éE   r  r  é   r  r  r/  r  r  r  r.  éY   é>   r	  é   é&   é   rË   r§   r,  )r  é   r  r  r  é-   r  r  r  r  r
  éc   éa   éR   ræ   r.  r:  r  r(  é#   )r$  r7  r9  r  rŒ   r   é	   r  éZ   r<  r/  é)   r)  r,  r9  r+  r8  r  r  r  )rš   r2  r'  r(  r   é!   r   r,  r+  rp   r*  éK   r*  r/  r"  r  r4  r  rË   r  )rÌ   ræ   rx   r  r  é4   r  ry   é    é3   r	  r&  éO   r  r-  r"  r  é   rA  r  )r  r	  r5  r#  r,  r  r0  r  r  r§   r¨   é1   r  r   r6  r  rz   r  r  rE  )r  r<  éP   rH  rG  r#  r}   r  rx   r  é6   r<  rG  é/   rJ  r>  r=  r   r:  r  )rp   rH  r<  r  r  r  r9  r-  r9  r;  rp   r  é0   rC  r   r  r4  rJ  r;  r  )r4  r  éI   r!  rC  r*  r  r6  r   r  é\   r6  r;  r'  r  r  rG  r?  r  r9  )rx   rD  r  r  r  r  r-  r  ry   r@  r;  r  r  r  r  r9  r-  r  r1  r  )r  é8   r}   r  rF  r  rF  r4  r  r  r9  rK  rz   r}   rD  r  r  r=  éT   rD  )rA  rp   r%  rF  r  r>  é   r0  r  r  r.  r  r  rË   r  r  rP  r  r  r}   )r;  r7  r§   rC  r}   rx   r  rQ  rC  r  r  r<  r@  rM  rE  rF  r  rz   r<  r  )r  r  rC  rŒ   rŒ   r  rO  r  r<  ry   r  rL  r}   rG  r¨   r7  r  r  r*  rC  )r6  r3  r+  r)  r  rC  r?  r"  r  r   r  rË   r,  r  rL  r  r  r$  rQ  rz   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   )rì   Úsymsrû   rü   Úx2Úx3Úx4Úx5Úx6Úx7Úx8Úx9Úx10Zx11Zx12Zx13Zx14Zx15Zx16Zx17Zx18r²   r–   rj   rt   rt   ru   Ú(test_linear_system_symbols_doesnt_hang_2Æ  s‚   í2ÿþýüûúùø	÷
öõôóòñðïír]  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sIJ ‚d S )Nrr   )r}   rx   r   r}   r}   rz   rx   rˆ   r˜   rŽ   r7  r§   r   )r   r>   rJ   ri   rj   rk   )rr   rì   rt   rt   ru   Útest_linear_systemLUý  s   *"þr^  c                     sb  ddl m} m} tttƒd tƒtdƒgksJ ‚tt| t | ttƒd  tƒƒ| |  tdƒhks4J ‚tttƒt	 tƒt
t	ƒ dt  t
t	ƒgksLJ ‚tdttƒ t	 tƒt
t	d ƒ dt  t
t	d ƒgksjJ ‚ttttƒttƒƒtƒtd gks}J ‚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 sòJ ‚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s&J ‚ttdt ƒd tƒtddƒgks:J ‚tdtd  tƒg ksHJ ‚tddt  tƒg ksVJ ‚ttdt  tƒttdƒƒ tdƒ gksnJ ‚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s—J ‚tdt tdt ƒ tƒttddƒƒd gks±J ‚ttdt d	 d	ttƒ  tƒƒtd
ƒtd	ƒtt  hksÑJ ‚dtdt d ƒ d ‰ tˆ tƒ}t|ƒdkrõt‡ fdd„|D ƒƒs÷J ‚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s&J ‚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sÒJ |ƒ‚tˆ  ¡ tƒ|ksÞJ ‚ttttƒ t	 tƒt
t	t ƒ dt  t
t	t ƒgksýJ ‚tttdt ƒ t	 tƒt
t	t ƒ d t t
t	t ƒd gks J ‚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srJ ‚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 sÑJ ‚tt	| t|   tƒt	|  d|  gksèJ ‚ttt t	 tƒtt	ƒttƒ gksýJ ‚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s%J ‚ttt	 gƒtdit	digks7J ‚ttt	 d ƒtdit	digksJJ ‚ttt	 d gƒtdit	digks^J ‚ttt	 td t	d   ƒtditt	 itt	it	digks~J ‚ttt	 td t	d   gƒtditt	 itt	it	digksŸJ ‚tttdƒt ƒdt  tƒdgks´J ‚tttdƒt ƒttdƒt ƒ tƒdgksÍJ ‚tdƒ‰tt	ˆtdƒt ƒ t	ˆtdƒt ƒ  tƒdgksîJ ‚tˆtƒˆdƒ tƒdgksÿJ ‚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sUJ ‚tdddd\} }ttt| d tt| ƒd  ƒ|ƒƒd!ksuJ ‚tt	dt  t tƒtt	ƒttƒ gksŒJ ‚tdt ƒtdt ƒtttd  ƒfD ]'}tttƒtdƒd  |t	 gƒ}|d t	 |d t	  jsÅJ ||fƒ‚qŸttd"t ƒtj ƒtd# td$ gksÝJ ‚tttd"t	  ƒd tƒd"t	 d"t	 dt  gksùJ ‚tttt	 t ƒd tƒt	 t t	 t dt  gksJ ‚ttttd  ƒƒt d dt d gks/J ‚d S )%Nr   ©ra   rb   rz   rx   rˆ   r¨   ry   iíÿÿÿræ   éüÿÿÿc                 3   ó(    | ]}ˆ   t|¡jd ddkV  qdS ©T)Zchopr   N©rÏ   ri   rr   ©r’   ra   ©r…   rt   ru   r—   *  ó   €& z,test_solve_transcendental.<locals>.<genexpr>r}   r   rÌ   r>  ia	  rË   rŒ   r€   c                      s   t ˆ ttƒˆ ddƒ tƒS ©Nr}   rx   r‘   rt   ©r€   rt   ru   r   f  rž   z+test_solve_transcendental.<locals>.<lambda>c                      s   t ˆ ttƒˆ dt dƒ tƒS ©Nrx   r‘   rt   rh  rt   ru   r   g  ó    c                      s   t ˆ ttƒˆ dt ƒ tƒS ©Nr}   r‘   rt   rh  rt   ru   r   h  s    c                      s   t ˆ ttƒˆ dƒ tƒS rk  r‘   rt   rh  rt   ru   r   i  ó    c                   S   s0   t ttƒtttƒƒ ttƒtttƒƒ  d ƒS ©Nrz   )rF   r(   ri   r'   rt   rt   rt   ru   r   o  ré   c                   S   s   t td t t d tƒS ©Nrx   rz   r‘   rt   rt   rt   ru   r   s  rž   za, bTF)ró   Únegativeç      à?zP[2.0 - 0.318309886183791*acos(1.0 - 2.0*a), 0.318309886183791*acos(1.0 - 2.0*a)]éè  i¸  éX  ) Ú	sympy.abcra   rb   rF   r$   ri   r%   r¥   r3   rj   r/   r   r   r5   r-   r   r#   r   r   rÞ   r¬   Úexpandrk   r0   r   r_   r„   r°   r   ÚstrÚis_Rationalr¸   )ra   rb   r•   Úresultrû   rü   rT  rU  rV  rW  rX  rY  rZ  r[  r\  Úyir²   rt   )r…   r€   ru   Útest_solve_transcendental
  sÆ    80<&þþ""þ
ú"	$"(0 (
ÿ4@
*<"(

$ü>F,&þ.F2F.*."$&(@B*2:"&""
ÿ.* ,,8<4ry  c                  C   sŠ  t dƒ} tdƒ| ƒ}tdƒ| ƒ}tdƒ\}}}}}}t|| ||  | || ||  | g||ƒ}	|	||| ||  || ||   ||| ||  || ||   iksXJ ‚t|d |ƒdgksdJ ‚td| d |ƒtddƒgksuJ ‚t|| | ¡ || | ¡  | || | ¡ || | ¡  | g| | ¡| | ¡ƒ}	|	| | ¡|| ||  || ||   | | ¡|| ||  || ||   iksËJ ‚t| | ¡d | | ¡ƒdgksÝJ ‚td| | ¡ d | | ¡ƒtddƒgksôJ ‚d| d d| d h}
t|
||hƒ|tddƒ|diksJ ‚t dƒ}td	ƒ}|d ||ƒd  d|  d }t| |¡t||ƒ|ƒƒ| d ||ƒ gksEJ ‚t dƒ}tdƒ| ƒ}t|| || | ¡  | || || | ¡  | g|| | ¡ƒ}	|	| | ¡|| ||  || ||   ||| ||  || ||   iksšJ ‚t dƒ}td	ƒ}t||ƒ |¡||ƒ |d¡ d ||ƒ |¡||ƒ |d¡ g||ƒ |¡||ƒ |d¡ƒ}	|	||ƒ |d¡tdƒd ||ƒ |¡tdƒd iksïJ ‚t||ƒ |d¡||ƒ |d¡ d d||ƒ |d¡ ||ƒ |d¡ d||ƒ |d¡ g||ƒ |d¡||ƒ |d¡ƒ}	|	||ƒ |d¡d
||ƒ |d¡diksCJ ‚d S )Nrl   ri   rj   rµ   r}   rz   rx   rˆ   r€   r   )r   r   r   rF   r   r   r   )rl   ri   rj   rº   r»   r¼   r½   r¾   r¿   ÚsolnÚeqnsr€   ÚFrt   rt   ru   Ú$test_solve_for_functions_derivatives  sn   0  
þ",ÿÿÿ(&
ÿ$.& 4 ÿÿ
ÿ( ÿ@ÿ<6ÿÿÿ2r}  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 s8J ‚d S )Nr€   rx   rˆ   r}   )r   ri   r   rF   )r€   r|  re   rt   rt   ru   Útest_issue_3725À  s    
Br~  c               	      sØ  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sxJ ‚t|| ||  g| |||gƒ| ||tddƒ| iks•J ‚t|| ||  g| |||gƒ| || |tddƒ| iks´J ‚t|| ||  || ||  g| |||gƒ| ||d	|d	iksÕJ ‚tt|| || ƒg| |||gƒ| ||tddƒ| iksóJ ‚tt|| || ƒg| |||gƒ| || |tddƒ| iksJ ‚tt|| || ƒt|| || ƒg| |||gƒ| ||d	|d	iks8J ‚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 drx   )r   rx   rŽ   r   )r}   rx   rz   rˆ   r}   r˜   rz   r~   r   zm nÚAri   rb   c                      s
   t ˆ ˆƒS r   )rF   rt   ©Zgrad_fri   rt   ru   r   â  ó   
 z#test_solve_Matrix.<locals>.<lambda>)
r   r>   rF   r   r   r?   ÚTr   r_   r°   )ra   rb   rc   rd   r€  ÚBÚCrn   rr   rÔ   r€   rt   r  ru   Útest_solve_MatrixÇ  s*   8:::>B<BH

r†  c                  C   sJ  t dƒ} tttƒdksJ ‚tttgddksJ ‚tt| gddks#J ‚tttdt  ƒttd ftdt ffv s:J ‚tttdt  tgdtdt fksNJ ‚tdt t dƒttd ftdt ffv seJ ‚tdt t dtgƒttd fksxJ ‚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sœJ ‚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sÏJ ‚tttƒd ttƒd  d t tgddksèJ ‚tttdƒƒtdfksõJ ‚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s3J ‚ttttd  ƒ tgdtdfksHJ ‚tdt d ƒdt d dfks[J ‚tddtd   ƒtdfkslJ ‚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sœJ ‚tt	dd„ ƒ d S )NÚw©r   r}   r¢   ©r   rx   rz   r   r}   r~   ©r   r   r˜   c                   S   s   t ttdƒdƒS rm  )rG   r   ri   rt   rt   rt   ru   r   ÿ  ó    z#test_solve_linear.<locals>.<lambda>)
r   rG   ri   rj   r3   r5   r   r$   r_   r°   )r‡  r…   rt   rt   ru   Útest_solve_linearå  s6   .(.&&""ÿ2*4*&"$rŒ  c                  C   sX  t ttd  ttd   tt  dt t  t d tttgtƒtdtdtdiks+J ‚t tt ttd   dt d td t   ttgtƒtdtdiksOJ ‚t td t td  td t td   td t t  td d t t  td d  td  tttgtƒtdtdtdiksJ ‚ttt ttt  } }}t|  t|  t|  |  d|  d|  }tttf}ttf}t ||ƒtdtdtdiksÌJ ‚t |||ƒtdtdtdiksÜJ ‚t ||g|¢R Ž tdtdtdiksïJ ‚t tt t d tgƒg ksÿJ ‚t td t dt  tgƒtditdigksJ ‚t dtgƒg ks#J ‚t dtgdd	g ks0J ‚t dtgdd
g i fks?J ‚t dtgƒg ksJJ ‚tt dt  t d }tth}t ||tƒtdtdiksiJ ‚t ||tdd
ttgdhfks{J ‚t ttt ƒtdt ƒ tfƒd u sJ ‚t tt tt  dt  ttfƒtdt iksªJ ‚d S )Nrx   r}   r~   r˜   rz   rˆ   r   Tr{   r¤   )rx   rz   )rK   ra   ri   rb   rc   rj   r5   )ÚXÚYÚZr…   ÚcoeffsrS  ZabeqrÓ   rt   rt   ru   Útest_solve_undetermined_coeffs  sj   <ÿþÿÿ
ÿ&ÿÿ
ÿÿ
ýü,

ÿ

ÿ
ÿ ÿ$*8r‘  c               
   C   sš  t dƒ} ttj| k | tk ƒ}t| d dkƒ|ksJ ‚t| d dkgƒ|ks'J ‚t| d dkg| ƒ|ks5J ‚t| d dkg| gƒ|ksDJ ‚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s~J ‚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s¸J ‚t| d | d  dk | ƒttd| ƒt| dƒƒksÒJ ‚t| | d  dk| ƒttt | ƒt| dƒƒksëJ ‚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s1J ‚tt
| dk dƒƒtj| k| tk @ ksFJ ‚tt
| dk dƒƒt | k | dk @ ks[J ‚tt
d| ƒƒdksgJ ‚tt
d| ƒƒdgkstJ ‚tt
d| ƒƒdks€J ‚tt
d| ƒƒdgksJ ‚tt
d|  ƒƒdksšJ ‚tt
d|  ƒƒdks§J ‚ttd| ƒƒdks³J ‚ttd| ƒƒ| t k| tk @ t| dƒ@ ksËJ ‚d S )Nri   r}   rx   r   r˜   Trò   rz   r   ry   F)r   r<   r   r·   r   rF   r   r   r=   r-   r   r5   r¸   r   r   r¶   r   )ri   r²   Úsystemrt   rt   ru   Útest_solve_inequalities*  sD   $ÿÿÿ$6ÿ428****4r“  c               	      sÈ  t dt ƒg ks
J ‚t tddt   ƒdgksJ ‚t tttƒ d ƒdgks(J ‚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sVJ ‚t ttd  d d ƒg ksfJ ‚t tttd d ƒ tƒdgksxJ ‚t ttƒt tƒttƒgksˆJ ‚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 s³J ‚dddt d   d	 ‰ t ˆ tƒ} t| ƒdkrÕt	‡ 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s0J ‚t td ddtd    ƒg ksCJ ‚t ttt
  t tƒdgksTJ ‚ttdd„ ƒ ttdd„ ƒ d S )Nr}   ry   rx   rz   r~   r   r˜   rˆ   rÌ   c                 3   ra  rb  rc  rd  re  rt   ru   r—   ^  rf  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$   rt   rt   rt   ru   r   e  ó    z!test_issue_4793.<locals>.<lambda>c                   S   s   t dt ttƒ d ƒS rn  )rF   ri   r$   rt   rt   rt   ru   r   f  rl  )rF   ri   r-   r$   rj   r%   r5   r3   rÞ   r¬   rk   r_   r„   ©r•   rt   re  ru   Útest_issue_4793Q  s,   .. $ B
&&8þB&"r–  c                  C   s8  t ttƒƒt ttd ƒƒ  krdgksJ ‚ J ‚t ttd ƒƒdgks&J ‚tdƒ} t d|  ttƒ tƒg ks9J ‚t dt td  d tƒdgksKJ ‚tt td dt   t¡ƒƒtjtdƒhkscJ ‚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sšJ ‚t ttƒtttƒƒ d ƒt	ddƒtdƒd  d gks¸J ‚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s2J ‚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sdJ ‚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 sªJ ‚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sJ ‚d S )Nrz   r   r}   ra   rŽ   rx   rÌ   rQ  r€   ry   r>  i´~ûÿi©æ  rˆ   r˜   r/  r`  rh   T©Úpositive)rF   r-   ri   r   r¥   r   r   r·   r   r   r,   rA   r$   r%   rj   rk   ÚExp1r   )ra   r€   r   rh   rt   rt   ru   Útest_PR1964i  sF   2$0:,<(((&ý
ÿ  
ÿ :
ÿ<ÿ.
ÿDDþ&rš  c                  C   sŒ  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s0J ‚t ddd} t d	ƒ}t| d
|  d d|  d|  d g| |ƒg ksTJ ‚t| | d|d  g| |ƒtdƒtdƒ fgksnJ ‚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sÄJ ‚d S )Nri   Trò   rx   r}   rr   ©Úintegerr˜  r—  rj   ry   rŽ   r   rp   r{   zx y z)r   rF   r-   r$   r   )ri   rr   rj   rk   rt   rt   ru   Útest_issue_5197–  s   ,44>Tr  c                   C   s¸   t ttttt   tddƒttƒtjttƒ hksJ ‚t ttttt   tddƒttƒttƒ hks6J ‚tddt d  dtd  d fƒg ksLJ ‚tddt d  ƒg ksZJ ‚d S )NFrÊ   Tr}   rx   rz   )r¥   rF   ri   rj   r-   r   r·   rt   rt   rt   ru   Útest_checking¨  s   ÿÿ4, rž  c               	   C   sz  t ttd d ƒd ƒtdƒtdƒ gtdƒ tdƒgfv s J ‚t dttd t ƒ d td d  tƒtttdtt tdƒ  ƒ ƒ tttdtt tdƒ  ƒ ƒgksXJ ‚tdƒ\} }t	dƒ}t | |td   t|tƒ ƒ |tƒƒttd | td  |  ƒgks‡J ‚t
dƒ}tj}t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv sÅJ ‚t t|d	 td  ƒ| tƒtd
|d	  ƒ td
|d	  ƒgtd
|d	  ƒtd
|d	  ƒ gfv søJ ‚t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv s0J ‚t |d d t|t ƒt|t ƒ  tƒt d|  gksPJ ‚t dt|t ƒt|t ƒ  tƒtdƒ| gkskJ ‚tt dt|t ƒt|t ƒd   tƒƒtdtdƒ ƒ| ttdƒ d ƒ| ttdƒ d ƒ| tdtdƒ ƒ| hks«J ‚t ttƒd ƒtdƒgks»J ‚d S )Nrx   r}   ry   rp   zC1 C2r€   ra   rˆ   rŽ   r˜   rz   r~   )rF   r-   ri   r$   rj   r%   r   r   r   r   r   r   r™  r5   r3   r(   r'   r¥   r1   r6   )ZC1ZC2r€   ra   r   rt   rt   ru   Útest_issue_4671_4463_4467²  s>   &
ÿ(>
ÿJ$$
þ  
þ$$þ@6(&&ÿ
ÿ$rŸ  c               	   C   sH  t dƒ\} }tt| td  td  t|ƒtt  gttgƒƒt| t|ƒd  ƒ dt| t|ƒd  ƒ t|ƒ ft| t|ƒd  ƒt| t|ƒd  ƒt|ƒ fhksTJ ‚tttƒt	tƒ dt d gttgƒt
t	tddƒƒƒtddƒfgksxJ ‚tttƒt	tƒ dttƒ d gttgƒt
t	t
dƒƒ ƒt
dƒ fgksžJ ‚ttttƒt	tƒ td d gttgƒƒt
t	dƒ ƒtdƒ ft
t	dƒƒtdƒfhksËJ ‚ttƒd t	tƒ td  dttƒ d g}t|ddttgt
dƒ ttdt ƒ t	t
dƒƒ ƒft
dƒ ttdt ƒ t	t
dƒƒ ƒ fhfksJ ‚t|ttddttgtttdt ƒ t	tƒ ƒftttdt ƒ t	tƒ ƒ fhfksEJ ‚tt|ttƒƒt
ttd  t	t
dƒƒ ƒ ƒt
dƒ ft
td  t	t
dƒƒ ƒd t
dƒ fhksyJ ‚tt|ttƒƒt
dƒ ttdt ƒ t	t
dƒƒ ƒ ft
dƒ ttdt ƒ t	t
dƒƒ ƒfhks­J ‚ttƒd t	tƒ t dttƒ d g}t|ddttgt
dƒ tdt ƒ t	t
dƒƒ fhfksáJ ‚t|ttddttgttdt ƒ t	tƒ fhfksþJ ‚tt|ttƒƒt
tt t	t
dƒƒ ƒ ƒt
dƒ ft
t t	t
dƒƒ ƒd t
dƒ fhks.J ‚t|ttƒtdt ƒ t	t
dƒƒ t
dƒ fgksJJ ‚tttd td  ƒtd	ƒ tt d fddttgtjtdƒftdƒtjfhfkswJ ‚ttttd td  ƒtd	ƒ tt d fttƒƒtjtdƒftdƒtjfhks¢J ‚d S )
Nzr,trx   r˜   r}   rz   rˆ   Tr¤   rŒ   )r   r¥   rF   ri   rj   r6   r-   r3   r$   r5   r%   r   r   rk   r¶   )rÔ   rl   r–   rt   rt   ru   Útest_issue_5132Ï  sr   02ÿ.þÿ$ÿ(ÿ(*ÿ,
&(þ
ÿ<þ(&þ
ÿ(&þ
ÿ("ÿ ÿ$"þ
$
ÿ. ÿ2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sMJ ‚tt||ƒƒdksXJ ‚d S )Núlam a0 concç{®Gázt?çÌ«¢Ã;Êç?rx   r}   T)ÚmanualZminimal©r   rj   ri   rÞ   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sLJ ‚d S )Nr¡  r¢  r£  rx   r}   F©Zrationalr¥  r¦  rt   rt   ru   Ú_test_issue_5335_float  s   ."
þ
rª  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s"J ‚d S )Nrx   rˆ   )r¥   rF   ri   rj   r-   rt   rt   rt   ru   Útest_issue_5767  s    ÿr«  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)ró   r˜  zSigma_f, Sigma_a, nuri   rx   rz   iÁ‡ i'  r   r}   ræ   rÌ   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   >"ÿFþÿ
r²  c                  C   sP   t ƒ \} }}t| |dd|gksJ ‚t|  ¡ |ƒ\}t|| ¡  ƒdk s&J ‚d S )NT©r¦   g›+¡†›„=)r²  rF   rr   Úabs)r…   r±  ri   Z	solapproxrt   rt   ru   Útest_issue_24609'  s   rµ  c                  C   s(   t ƒ \} }}tt| |ƒƒ|gksJ ‚d S r   )r²  rÞ   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s7J ‚ttd t d td t gƒg ksKJ ‚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ssJ ‚d S )Nrx   rz   r}   ry   rˆ   )r¥   rF   ri   rj   r   r¶   r-   rt   rt   rt   ru   Útest_polysysD  s   ,"ÿÿ(,ÿÿ
ÿÿr·  c            	   
      s´  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 s(J ‚| tttƒƒtg fƒs5J ‚| tttƒd
 ƒtd
 g fƒsFJ ‚| tttƒttdƒ d ƒˆd ˆd  d ˆˆd t gfƒshJ ‚| 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sžJ ‚| tttƒttd
 ƒ tdt ƒ ƒdtdƒ t dt  d
 g fƒsÃJ ‚| tttƒttd
 ƒ d ƒdt d g fƒsÜJ ‚| tttƒttd
 ƒ td
t ƒ ƒdtd  dt  g fƒsýJ ‚| 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s9J ‚| tttƒtd
t ƒ ƒdt d
 g fƒsQJ ‚| tttƒtd
t ƒ d ƒtd t d g fƒsmJ ‚| 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 sÞJ ‚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sJ ‚| 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sPJ ‚tt|d"d#ƒtjtddƒhkscJ ‚t|ƒg kslJ ‚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sJ ‚| 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sÚJ ‚| tttd
t  ƒdttƒ  tƒdt t t dt  g fƒsýJ ‚| 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sRJ ‚ttttdt d ƒd tƒƒƒtj tdƒhksnJ ‚ttttdt d
 ƒttd ƒ dƒƒƒtdƒtd%ƒhksŽJ ‚ttttd& ƒd tdt ƒƒƒd'gks¥J ‚tdt d td
dƒ d ƒdgksºJ ‚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sÞJ ‚tttdtd  d& ƒdt  ƒƒtdƒ tdƒhksüJ ‚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s6J ‚tttƒttd& ƒ d* ƒdgksJJ ‚tttd ƒttƒ d ƒdgks^J ‚ttdtd  d ƒdt d  ƒd)gksvJ ‚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sÓJ ‚tttƒttd
 ƒ tttƒƒ ƒg ksêJ ‚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sJ ‚t|dt  ƒtd(d/ƒgks'J ‚t|dt  ƒg ks4J ‚tttd
 dƒttdƒ ƒtd td  dtd   dt  d
  g fks\J ‚| 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s®J ‚tttƒttdƒ d ƒd
gksÁJ ‚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sEJ ‚ttd
 dƒttdƒ }t|ƒdt d
 g fks`J ‚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sšJ ‚| tttdƒttdƒd  d
 ƒˆd ˆ d
 ˆˆd t gfƒs¾J ‚| tttdƒttdƒd  d
 ƒtd dtd   t d
 g fƒsâJ ‚ttd< ƒd u síJ ‚| 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sJ ‚| 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sBJ ‚| 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sqJ ‚| 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sÐJ ‚t td=d„ ƒ tttdƒttdƒ d ƒd
gksëJ ‚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s%J ‚tdBƒ‰ t|ƒˆ ks2J ‚| 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sdJ ‚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s¨J ‚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sðJ ‚| 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	sxJ ‚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	s¼J ‚ttdRƒƒd u 	sÇJ ‚| ttdRƒtƒˆdt  ˆ d
 ˆˆd t t gfƒ	sæJ ‚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
sJ ‚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
sKJ ‚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s¾J ‚| 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sJ ‚| 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sëJ ‚tttƒttd
 ƒ td
t ƒ tdt ƒ ƒ‰ tˆ ƒd
krt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 ]"}ttt  t|¡ t¡td"d"dt}t‡ fdudv„|D ƒƒrl nqKJ ‚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s J ‚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sTJ ‚t|ƒg ks]J ‚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s’J ‚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sqJ ‚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 s¨J ‚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sÏJ ‚t|ƒd u sØJ ‚d S )ˆNc                   S   s,   t ttƒttd ƒ tdttƒ ƒ d ƒS ©Nr}   rz   )rP   r-   ri   rt   rt   rt   ru   r   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}   rz   rx   )rP   r-   ri   r   rj   rt   rt   rt   ru   r   R  ó   *rÓ   )Úclsc                    sd   t | d ƒt |d ƒksJ ‚|d rˆ | |ƒS | d  ¡ }|d  ¡ }||| fv o1| d |d kS ©Nr}   r   )Úboolrt  )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 okt| d ƒt|d ƒkS )Nr   r}   )r®   Úatomsr   ÚziprÞ   rÏ   rt  ru  )r½  r•   rd   Úreps©rÓ   rt   ru   r¾  a  s   66&ÿztest_unrad1.<locals>.s_checkr}   rz   rx   r   ry   r   r~   r¨   r>  rˆ   r-  ix  iè  ià  i  ræ   iÜ  iæ	  i¼  é©   r@  r  éè   é    FrÊ   z32*sqrt(x)*(x + 1)**(1/3) + x - 4*y + (x + 1)**(2/3)r  rÌ   iúÿÿÿr˜   r   r§   rH  rŒ   rÄ   r/  r
  c                   S   s(   t ttƒttdƒ ttd dƒ d ƒS )Nrz   r}   ry   rx   )rF   r-   ri   r,   rt   rt   rt   ru   r   É  s   (c                   S   s   t tdƒ ttƒt  ƒS ri  )rF   r-   r'   ri   rt   rt   rt   ru   r   Ì  rž   r  r8  éÔ   éÀ   rO  i	=  iÈ£ im i { i  rp  c                   S   s6   t ttdƒttdƒ ttdƒ  ttd t d ¡ƒS )Nrx   rz   rˆ   ry   r}   )rP   r,   ri   rÏ   rt   rt   rt   ru   r   æ  s   6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)]r  rI  r5  rG  T)Z_reverserQ  rM  é»   é  éä   r3  r  rD  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 - 1r2  i   iW  i   iÀ  rL  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0.73r|  ©r¦   r«   c                 3   s    | ]
}|ˆ    ¡ jV  qd S r   )rt  Úis_zerord  r•  rt   ru   r—   K  ó   € 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™   rE  éf   iT  i06  r7  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 )Nrz   ry   )rP   r,   ri   rj   rt   rt   rt   ru   r   q  s   & )!r_   r„   r   r   rP   r-   ri   r,   r   ra   rb   rc   rj   rd   r   r¶   r¥   rF   r·   r   rR   r   rl   r'   r¸   rÞ   rv   r   ÚreversedrÏ   r   Úanyr$   )	r«   r…   rk   rh   re   r|  r  ÚxirŽ  rt   )r•   rÓ   r¾  ru   Útest_unrad1N  s0  ÿ
ÿ"ÿÿÿ$ÿÿ$ÿ4:
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ÿ
ÿÿÿÿ
ÿ2:
ÿ
ÿ
ÿ
ÿ
ÿ
þþþþ
ÿ
ÿ
ÿ,("ÿ,40Fÿ*ÿ
ÿþþþý"ÿÿÿý
ÿ:
ÿ"Bÿÿÿÿþþþ
ÿÿVP
ÿ>$4rÙ  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s,J ‚d S )Nr}   rˆ   rx   )r-   ri   rF   r   r¸   re  rt   rt   ru   Útest_unrad_slow„  s   DrÚ  c                   C   s¬   t ttd dtd   dƒd t ƒtddƒgksJ ‚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sTJ ‚d S )
Nrz   rx   r}   ry   r˜   rˆ   ræ   rŒ   r   )rF   r,   ri   r   r[   rt   rt   rt   ru   Útest_unrad_failŒ  s   6&BÿrÛ  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 sMJ ‚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 skJ ‚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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 s¯J ‚tˆ d ˆ d d gˆ dƒdu sÁJ ‚tˆ d ˆ d d gˆ dƒdu sÓJ ‚ttˆ d d ƒˆ dƒdu sãJ ‚tdi ƒdu sìJ ‚tdˆ d gˆ dƒdu súJ ‚tddˆ gˆ dƒdu sJ ‚t| ˆ dƒdu sJ ‚tˆ d ˆ ddd	du s"J ‚tˆ d ˆ ddd	du s1J ‚ttd
ˆ  ƒˆ ttdƒd ƒiƒdu sGJ ‚ttd
ˆ  ƒˆ ttdƒd ƒt	t
  iƒdu saJ ‚tdˆ d  ˆ dƒdu spJ ‚tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nz
x, y, r, trx   r}   TFr   g»½×Ùß|Û=rp  ©Z	numericalrN  ry   rq  c                      s
   t ˆ dƒS rk  ©rQ   rt   rä   rt   ru   r   ®  r‚  ztest_checksol.<locals>.<lambda>c                      s   t g ˆ dƒS rk  rÝ  rt   rä   rt   ru   r   ¯  r¡   )r   r-   r6   rQ   r   r   rA   r$   r%   r   r   r_   r°   )rj   rÔ   rl   r…   Zdict_var_solnrt   rä   ru   Útest_checksol•  s6   &ÿ    ($$ ,4rÞ  c                   C   s¢   t td ƒdtfksJ ‚t dƒdksJ ‚t tdt ƒd tƒdtdƒ tfks)J ‚t tdt tt  ƒd tƒtd tdƒ tfksDJ ‚t ttƒtdfksOJ ‚d S )Nrx   )rx   r   r}   rz   r   )rO   ri   r$   r%   ra   rt   rt   rt   ru   Útest__invert²  s
   *6rß  c                   C   sž   t t t dt ttƒ  tƒttd ƒgksJ ‚t tt ƒg ks#J ‚t tt d ƒtttdƒƒƒgks6J ‚t td td  td td   ƒdgksMJ ‚d S )Nrx   rz   rˆ   )rF   ra   ri   r%   r$   r#   rt   rt   rt   ru   Útest_issue_4463º  s   2&2rà  c                  C   s8  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sšJ ‚d S )Nza:rr}   TF)r¤  r«   r¦   )r   rÞ   rF   )ra   rb   rc   rd   re   r€   r   rg   rÜ   Újrf   Úlrn   rr   rô   rh   rm   rÔ   rS  r–   rt   rt   ru   Útest_issue_5114_solversÀ  s   ,****û"rã  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s¹J ‚t|gˆ¢R dddœŽ‡fdd„ˆ D ƒksÐJ ‚t|gˆ¢R ddiŽg ksßJ ‚t|gˆ¢R Ž g ksëJ ‚‡ 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~   rx   rz   r§   r`  ræ   rˆ   r   r  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getrÛ   rð   rt   ru   Ú
<listcomp>ñ  rl  z.test_issue_5849.<locals>.<listcomp>.<listcomp>©r­   )r’   )Úvrð   ru   rè  ð  s    ÿz#test_issue_5849.<locals>.<listcomp>r¤  c                    s   g | ]	}|  ˆ d  ¡‘qS ©r   )rÏ   )r’   Úeir•  rt   ru   rè  ÷  s
    ÿÿr   ©r   rF   ©ZI1ZI2ZI3ZI4ZI5ZI6ZdI1ZdI4ZdQ2ZdQ4ZQ2ZQ4re   rt   )r•   rê  ru   Útest_issue_5849Ð  s@   


*÷$ù	" ÿ
ÿÿrï  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spJ ‚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.
    rä  rå  r~   rx   rz   r§   Nrí  rî  rt   rt   ru   Útest_issue_5849_matrixû  s   



*÷$rð  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sÕJ |
|	fƒ‚d S )Nza, b, c, d, f, g, kry   r   rx   r>  rˆ   rz   r  r7  rË   r   r~   Tr{   )r   r   rF   )ra   rb   rc   rd   r€   r   rf   ZunknownsZ	equationsZanswerÚgotrt   rt   ru   Útest_issue_21882  s"   <" ÷$&ýrò  c                     sŽ  t tdƒ\‰ } }tdƒ}tˆ tƒtƒ}t| |ƒ|ƒ}tˆ tƒˆ tƒ t¡ ˆ tƒƒ| gks0J ‚tˆ tƒd ˆ tƒƒdgks@J ‚tˆ tƒdˆ tƒ t¡  ˆ tƒƒd| gksYJ ‚tˆ tƒdˆ tƒ t¡  gˆ tƒƒˆ tƒd| iksvJ ‚tˆ tƒdˆ tƒ t¡  ˆ tƒd t d gˆ tƒtƒd| d|d  d fgks¢J ‚tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒdd||ƒ| |ƒgtˆ |ƒd | |ƒd  | ƒ ˆ |ƒ | |ƒftˆ |ƒd | |ƒd  | ƒˆ |ƒ | |ƒfhfks2J tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒddƒ‚ˆ tƒ td¡ˆ tƒ| tƒ  d| tƒd  gˆ tƒ| tƒg}t|d	diŽd
 tdƒ tdƒftdƒtdƒ fhksoJ ‚ˆ tƒd | tƒ dˆ tƒ t¡  | tƒd d g}t|ˆ tƒ| tƒddˆ tƒ| tƒgtd| d ƒ t	dƒftd| d ƒt	dƒftd| d ƒ t	dƒ ftd| d ƒt	dƒ fhfksÓJ ‚t
t‡ fdd„ƒ tˆ tƒˆ tƒ t¡ tgdˆ tƒtˆ tƒtƒ d
fksüJ ‚tˆ tƒttttfƒ tgdˆ tƒttttfƒ d
fksJ ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ d
fks@J ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ fkscJ ‚ttˆ tƒ|  ˆ tƒd
 |  tgdtd
| fksJ ‚tttdt tƒ ƒtdfks“J ‚tttttƒ tgdtdfks¦J ‚tttttƒ d tgdtdtd
  fks¿J ‚tttttƒd  ttƒƒƒtt ƒ tt ƒhksÜJ ‚ttttƒ tddttƒ gksðJ ‚tttƒttƒ tddg ksJ ‚ttttƒ tddttƒgksJ ‚ttd t d tddtd  d gks-J ‚ttd t d td ddt d gksEJ ‚d S )NZfghra   rz   rx   rˆ   r>  Tr¤   r¥   r}   c                      s$   t ˆ tƒˆ tƒ t¡ ˆ tƒgdS )Nr‰  )rG   ri   r   rt   rh  rt   ru   r   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$   r3   r5   )r   rg   ra   r­  ÚGr³   r–   rt   rh  ru   Útest_issue_59010  s®   ÿÿ"ÿ$ÿ8ÿ@ÿ0.þþ@ÿü>"
ÿ6ü
ÿÿ
ÿ
ÿ"
ÿ"
ÿ(

ÿ
ÿ
ÿ
ÿ
ÿ

ÿ$
ÿ
ÿ
ÿrô  c                  C   sº   t ttd t d ddƒtjtdƒd  tdƒ d tj hks#J ‚ttd t d dd} t| ƒdkr>tdd	„ | D ƒƒs@J ‚ttd t d ƒ} t| ƒdkrYtd
d	„ | D ƒƒs[J ‚d S )Nrx   çš™™™™™¹?Tr©  r=  rŒ   Fc                 s   ó    | ]}|j V  qd S r   ©Z	is_Numberrd  rt   rt   ru   r—   x  ó   € z"test_issue_5912.<locals>.<genexpr>c                 s   rö  r   r÷  rd  rt   rt   ru   r—   z  rø  )r¥   rF   ri   r   r¸   r-   rÞ   r¬   r•  rt   rt   ru   Útest_issue_5912t  s   $ÿ"&rù  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s,J ‚t td d dd js9J ‚t ttj d dd jsGJ ‚| tdd	t  ƒd
dt  ƒsXJ ‚ttt	fD ]"}t|dd	t  gƒƒ}t
|ƒ|u r}| t|ƒd d
dt  ƒsJ ‚q]ttd	t dd	t  giƒ ¡ ƒd \}}| |d	t ƒr§| |d d
dt  ƒs©J ‚| ttd	t ƒƒtdt ƒƒsºJ ‚| tdtd	  ƒdtd	  ƒsËJ ‚| tdtd	  dddtd  ƒsÞJ ‚| ttd	t ƒƒtdt ƒƒsïJ ‚| ttd ƒtd ƒsüJ ‚| ttd d	t  ttddƒƒ d ƒtd dt  d ƒsJ ‚dt t t }t dt | d dt | d t| d fƒg ksAJ ‚d S )Nc                 S   s   t |  t¡ƒt | t¡ƒkS r   )rÞ   r¿  r   ©Úe1Úe2rt   rt   ru   Útest~  s   z!test_float_handling.<locals>.testrp  Tr©  r   Fr}   rx   ç      ð?g       @rz   g      @rÍ   rˆ   g!ÌÈ,‹ÿ?r¬  gffffffæ?g333333ã?gš™™™™™É?g333333Ó?rõ  )rF   ri   rv  Zis_Floatr   r¸   rH   r®   r­   r¥   ÚtypeÚitemsr3   r$   r   rc   rk   rl   )rý  Zcontainr•   rf   rê  Ztotrt   rt   ru   Útest_float_handling}  s,   ",*(""&"&
ÿ<r  c                  C   s*   t ddd} t| d d ƒdgksJ ‚d S )Nri   Tr—  rx   r}   rí  rä   rt   rt   ru   Útest_check_assumptions—  ó   r  c                   C   sì   t ttd ƒttd ƒ d ƒg ksJ ‚t ttd ƒttd ƒ d ƒtt tddƒ t t d tt d tt tddƒ gksCJ ‚t ttd ƒttd ƒ d d ƒtt tddƒ t t d tt d tt tddƒ gkstJ ‚d S )Nrz   r}   rŽ   rˆ   rx   )rF   r)   ri   r   r   r   rt   rt   rt   ru   Útest_issue_6056œ  s   (8ÿ"8ÿr  c                  C   sV   t  ttttt ƒƒƒttt ƒƒ ƒ } t| t dƒdu sJ ‚t| t dddd u s)J ‚d S )Nrx   TFrÜ  )ri   r$   r#   r%   rQ   re  rt   rt   ru   Útest_issue_5673¤  s   &r  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 sYJ ‚d S )Nz$R, C, Ri, Vout, V1, Vminus, Vplus, sÚRfTr—  r~   r}   r˜   r¢   rx   rz   r   ry   r   ©r   rF   r-   )
ro   r…  ZRiZVoutZV1ZVminusZVplusrÓ   r  r–   rt   rt   ru   Útest_excludeª  sL   ÿ"(ý$(üü
ú,@ü,@üû$ üör  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s)J ‚d S )Nry   rˆ   rz   rx   rÌ   ZZZ)Údomain)ri   r   r¥   rF   rA   Z	all_rootsrÂ  rt   rt   ru   Útest_high_order_rootsÒ  s   *,r
  c                     sÐ  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s&J ‚t tt d dt t d gfi |¤ŽtdtdiksBJ ‚dd	„ }|t tt t tt t t gfi | ¤Žƒdks`J ‚|t tt t tt t t gfi |¤ŽƒdkszJ ‚|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sªJ ‚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s*J ‚dD ]2‰ tdd„ t tt t tt t gˆ dd 	¡ D ƒƒrKJ ‚t
t‡ fdd „ƒ t
t‡ fd!d „ƒ q,t
td"d „ ƒ d S )#NT©ÚquickÚ
particularFry   rx   r}   rz   c                 S   s   t dd„ |  ¡ D ƒƒS )Nc                 S   s   g | ]}|d kr|‘qS rë  rt   )r’   ri   rt   rt   ru   rè  Ý  rl  z>test_minsolve_linear_system.<locals>.count.<locals>.<listcomp>)rÞ   Úvalues)Zdicrt   rt   ru   ÚcountÜ  rÃ   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©rœ  r~   r   ©r  c                 s   ó    | ]}|V  qd S r   rt   ©r’   rê  rt   rt   ru   r—   ö  ó   € z.test_minsolve_linear_system.<locals>.<genexpr>)TFc                 s   r  r   rt   r  rt   rt   ru   r—   ø  r  c                      s   t td gˆ dS )Nr}   )r  r    rt   ©Z_qrt   ru   r   ü  s    z-test_minsolve_linear_system.<locals>.<lambda>c                      s   t td gˆ ddS )Nr}   Fr  r    rt   r  rt   ru   r   ý  ó    c                   S   s   t td ddS )Nr}   Tr  r    rt   rt   rt   ru   r      r‹  )rF   ri   rj   rk   ra   rl   r>   r   r¬   r  r_   r°   )ZpqtZpqfr  r€  rê  r„  r–   rt   r  ru   Útest_minsolve_linear_system×  sR   

884400ô&ÿ4
þþr  c                  C   s4   t ddd} tt| d | d  d ƒƒdksJ ‚d S )Nri   Trò   ry   rz   r}   )r   rÞ   rF   rä   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s4J ‚d S )NicË†rx   iQÖAiTâkl   1ö'	 iýûa5iPQRiçäžl    d(	 FrÊ   rˆ   )ri   rj   rÞ   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s&J ‚t|| dd
tjfgks4J ‚t|| dddtjftdƒfgksGJ ‚d S )Nri   Trò   rˆ   rÌ   ry   rz   ræ   r}   ©r¤  Fræ  )r   r   rF   r   r¸   )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s9J ‚td	ƒttdƒƒ ttdƒƒ }td| d  dd|    ƒ| |gks^J ‚d S )
Nri   rˆ   rx   rz   r   Trò   ry   r   )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 )Nrx   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spJ ‚d S )Nrx   rˆ   ræ   r}   FrÑ  ry   )r-   rn   rm   r   r¸   r   rF   rÞ   ©r…   r²   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s0J ‚d S )Nrx   )r˜   r˜   rŠ  )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sYJ ‚d S )	Nr}   rx   r   r˜   r   rz   rˆ   ry   )rF   ri   r[   rt   rt   rt   ru   Útest_issue_67927  s
   *.((ýr!  c                     sj  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s2J ‚tttˆ d	 ƒd
 ƒƒtj tdƒhksHJ ‚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ssJ ‚tdtˆ ƒ tˆ d ƒ ƒdt
ddƒgksŠJ ‚ttˆ d ˆ  d ƒˆ d  ƒg ksžJ ‚ttˆ ƒƒdgks©J ‚tttˆ d dˆ   ƒdƒˆ ƒdtdƒ dtdƒ gksÇJ ‚t ddd}ttt|ƒƒƒdgksÚJ ‚t ddd}ttt	ddd|   ƒdƒƒt
ddƒ gksøJ ‚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sJ ‚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sTJ ‚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s›J ‚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sÌJ ‚t ddd‰ tˆ |  d dt  ƒˆ d| dt ikséJ ‚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s3J ‚d S )!Núx yTrò   rz   rx   r}   r>  )r~   rÌ   ræ   rp   r˜   r  r1  r   rˆ   ry   Únn)ZnonnegativeÚnz)Únonzeror¨   ri   rÜ   ©Z	imaginaryrŽ   c                      s   t tˆ ƒd ƒS rm  )rF   r´  rt   rä   rt   ru   r   b  r‹  zBtest_issues_6819_6820_6821_6248_8692_25777_25779.<locals>.<lambda>r‡  r  r~   r€   )r   rF   r´  r   r   r¥   r   r¶   r   r   r   r-   r¸   r"   r!   r   r_   r„   r   r%   )rj   r#  r$  r…   rÜ   r‡  r€   rt   rä   ru   Ú0test_issues_6819_6820_6821_6248_8692_25777_25779>  sP   ,(,&&
ÿ.(
ÿ0ÿ &:&6.,,0r'  c                   C   s  t dtdt ƒ ttƒ tdt ƒd d  dktƒt tk ttdƒd k @ ks*J ‚t dtdt ƒ d ttd ƒ ttƒd d  dktƒt tk ttdƒd k @ ksVJ ‚t ttƒd td  tdt d ƒ ttƒd d  dktƒt tk ttk @ ks€J ‚d S )Nrx   r   rˆ   )rF   r$   ri   r   r%   rt   rt   rt   ru   Útest_issue_17638z  s   TXXr(  c                  C   s0  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shJ ‚|||  |||   ||| |	|| ||  i}|D ]}| d |  ¡ ||  ¡ ks•J ‚qƒd S )	Nzs, tau_c, tau_1, tau_2, phi, Krx   r}   zK_C, tau_I, tau_DT)r˜  r%  r{   r   )r   ZtogetherrD   r¦   rA   r  rF   rÞ   )rÓ   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,   ÿ6ÿ

þ"ÿr.  c                     sd  ddl m‰ m‰ ttˆ dˆ   tˆ ƒ ˆ ƒˆ ƒˆ tˆ ƒhks!J ‚tˆ ˆ ƒg ks*J ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   ¡ƒt
dtj ƒd gksLJ ‚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sJ ‚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sµJ ‚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sJ ‚tt
dˆ  ƒˆ ˆ ƒˆtˆƒ d gks0J ‚d S )	Nr   ©ri   rj   r}   rx   rz   c                      s   t ˆ tˆ ƒtˆˆ  ƒ  ˆ ƒS r   )rF   r5   r%   rt   r/  rt   ru   r   «  rj  z+test_lambert_multivariate.<locals>.<lambda>rŽ   )rs  ri   rj   rL   rA   r$   rN   rF   rÏ   r%   r#   r   r™  r-   r_   r„   r¥   )r…   r•   rt   r/  ru   Útest_lambert_multivariateŸ  s"   2D20ÿ*6ÿ $" .2r0  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s5J ‚d S rm  )rF   r5   ri   r¥   ra   r#   r%   rt   rt   rt   ru   Útest_other_lambert²  s   ( ÿr1  c            
      C   sN	  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s6J ‚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snJ ‚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s¶J ‚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sèJ ‚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s&J ‚t td dt  tƒdddttdƒd ƒ tdƒ gksEJ ‚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sÒJ ‚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s1J ‚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sŒJ ‚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sÄJ ‚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sìJ ‚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s"J ‚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sfJ ‚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s­J ‚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s)J ‚t dtdttƒ d ƒd  t ƒttdƒ dƒd d gksKJ ‚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s¥J ‚d S )Nrx   r}   r˜   rˆ   rz   rŽ   r~   ry   éûÿÿÿr   i ØÿÿrÌ   iëÿÿÿr   rh   Tr—  r`  r{   )rF   ri   r$   r   r-   r#   ra   r   r%   rÞ   rt  r,   rÏ   r   rb   r   rM   rL   rA   r¥   r3   r/   rk   rj   r   )
r•   Úaxrû   rü   rT  rU  rV  rW  rh   r…   rt   rt   ru   Útest_lambert_bivariate¹  sÊ   "  
þ&  
þ28ÿþÿ
ÿ@>"2
ÿ$(
ÿ$ÿ"ý ý $ÿ&ÿ4,ÿ"ý 02ÿ
ÿ"(
ÿ8ÿ"ÿ"ÿ"úr4  c                   C   sŒ  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sJ ‚t ttƒttƒ ƒdt	t gks¯J ‚t dttƒ ttƒ tƒtt
jƒgksÄJ ‚d S )Nr   rx   r~   r˜   r}   rz   )rF   r5   ri   r6   r   r4   r1   r   r-   r   r   r¸   r(   r)   r3   rt   rt   rt   ru   Útest_rewrite_trig  s    *@Dÿÿÿÿ
ý$.r5  c                  C   sø   ddl m}  tttƒ| tƒ ƒdttddƒtdƒd  tdtdƒ d ƒd  ƒ dttddƒtdƒd  tdtdƒ d ƒd  ƒ dttdƒ d tj	 tddtdƒ  ƒd  ƒ dttddtdƒ  ƒ d tdƒd  tj	 ƒ gkszJ ‚d S )Nr   ©Úsechrx   r˜   ry   r~   )
Ú%sympy.functions.elementary.hyperbolicr7  rF   r(   ri   r&   r   r-   r   r¸   r6  rt   rt   ru   Útest_rewrite_trigh"  s   4422ür9  c                  C   s  t ttƒ tttdtd td     ƒ } t| tddttttt ƒ  ƒ ttttt ƒ  ƒgks4J ‚tttd ƒtddt  ƒ d ƒdtdtdƒ ƒttddƒƒ d  tdƒd  tdtdƒ ƒ ttddƒƒ d d tdƒd  gdtd	tdƒ d
 d  ƒd  tdƒd  dtd	tdƒ d
 d  ƒd  tdƒd  gfv s©J ‚tttdt ƒd ƒtttƒ d ƒ tdƒ ƒg ksÆJ ‚d S )Nr˜   rx   T)Úforcerz   r}   rŽ   iôÿÿÿiÜÿÿÿr   )	rk   r%   ri   rj   rF   r-   r$   r   r)   re  rt   rt   ru   Útest_uselogcombine-  s   ,<"02ÿ,,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 rn  )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s0J ‚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=  ó      $r=  c               	   C   sR  t dƒ} tdƒ|  td| d  ƒ | d tdƒtd| d  ƒ d   }t|| ddd }|tddƒtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ   ddtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ     ftddƒddtd	d
ƒtdƒt d  tddƒ    td	d
ƒtdƒt d  tddƒ  fhks§J ‚d S )Nro   rx   r}   Tr¤   ry   rz   r˜   éû   rÄ   éo   r>  r  )r   r-   rF   r   r   )ro   r…   r²   rt   rt   ru   Útest_issue_2725D  s,   @*ÿÿ$ÿÿÿÿÿ"ÿþrA  c                  C   sf  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s±J ‚d S )Nzb:rr}   Fr³  c                 s   s    | ]}|  ¡ V  qd S r   )Ú	count_ops)r’   rÓ   rt   rt   ru   r—   \  s   € z'test_issue_5114_6611.<locals>.<genexpr>iÆ  )r   r>   rF   r®   rö   r  )rb   rc   rd   re   r€   r   rg   rÜ   rá  rf   râ  rn   rr   rô   rh   rm   rÔ   r–   rê  r•   rt   rt   ru   Útest_issue_5114_6611N  s   *@\Lý"rC  c                  C   s    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s4J ‚tdddƒ}t|ƒt|ƒ  krK| ¡ ksNJ ‚ J ‚d S )Nrz   za:9r}   rŠ  r>  rx   )r}   rx   r}   rˆ   )	r>   r   ZdetrT   r®   rø   r@   rU   rV   )rn   rÓ   rt   rt   ru   Útest_det_quick_  s   ,rD  c                  C   s’   t ddd\} }tt| d |d  ƒd | ƒt|d  d ƒ t|d  d ƒgks,J ‚t ddd\} }tt| d |d  ƒd | ƒg ksGJ ‚d S )Nza bTrò   rx   rz   r>  r&  r  r_  rt   rt   ru   Útest_real_imag_splittingk  s   $ÿ*rE  c                  C   sB   dt d  dt d   dt   d } tdd„ t| ƒD ƒƒsJ ‚d S )Nr~   rz   rˆ   rx   ry   c                 s   s    | ]
}t t |¡ƒV  qd S r   )r   r   ró   rÛ   rt   rt   ru   r—   u  rÓ  z"test_issue_7110.<locals>.<genexpr>)ri   r×  rF   rØ   rt   rt   ru   Útest_issue_7110s  s   $rF  c                   C   s*   t dt ddt   ƒdt gksJ ‚d S rg  )rF   ri   rY   rt   rt   rt   ru   Ú
test_unitsx  r¹  rG  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sOJ ‚d S )NzA,B,Vg®Gáz²ƒ@g     €C@r  r   g    d6 Ag    0Œ!A)r   r   r   z4442890172.68209z4289299466.1432z70.5389666628177)r   r   r>   rE   r   ru  )r€  r„  r¯  Úeq1Úeq2Úeq3r²   rt   rt   ru   Útest_issue_7547|  s   &
þÿrK  c                  C   s*   t ddd} tt| ƒd ƒdgksJ ‚d S )NrÔ   Trò   rx   rˆ   r  )rÔ   rt   rt   ru   Útest_issue_7895ˆ  r  rL  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sHJ ‚t||| |  f| |fƒg ksYJ ‚|d
7 }t||f| |fƒg ksjJ ‚t||f| |fdd|ksyJ ‚d S )Nr"  Trò   rx   rŒ   rz   é¿   rË   i‡  r   FrÊ   )r   r-   r   rF   )ri   rj   rû  rü  ra   rb   r•   rt   rt   ru   Útest_issue_2777  s   8""rN  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   rP  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   r   ¡  s    ztest_nsolve.<locals>.<lambda>c                   S   s(   t tt d tt tt ftttfdƒS )Nrz   )iÎÿÿÿr  )rE   ri   rj   rk   rt   rt   rt   ru   r   ¢  s   ( c                   S   s   t tt tt fdƒS )Nrˆ  )rE   ri   rj   rt   rt   rt   ru   r   £  r”  c                   S   s   t tdk tdƒS )Nrp  r}   rS  rt   rt   rt   ru   r   ¤  r‹  )r_   r°   rƒ   rt   rt   rt   ru   Útest_nsolve   s   rT  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s&J ‚tttd  t d tƒg ks7J ‚ttdd„ ƒ td t d ‰ tˆ ddˆ    ƒ‡ fdd„tdƒD ƒks]J ‚td ‰ tˆ d	dˆ    ƒtjgksqJ ‚d S )
Nrz   r}   rˆ   ry   c                   S   s   t ttd  t d tddS )Nry   r}   F)Ú
incomplete)rF   ra   ri   rt   rt   rt   ru   r   ¬  rw   z.test_high_order_multivariate.<locals>.<lambda>c                    s   g | ]	}t ˆ d  |ƒ‘qS rR  rZ   rÛ   ©rd   rt   ru   rè  ²  rž   z0test_high_order_multivariate.<locals>.<listcomp>rx   )	rÞ   rF   ra   ri   r_   r„   rø   r   r¸   rt   rt   rV  ru   Útest_high_order_multivariate§  s   &&".$rW  c                   C   sX   t dt d ƒdgksJ ‚t dtd  d ƒdgksJ ‚t tdddƒddgks*J ‚d S )Nr   r}   rx   zx*(1/x**0 - x)F©Úevaluate)rF   ri   r   rt   rt   rt   ru   Útest_base_0_exp_0·  s
   ÿrZ  c                   C   sd   t dtd  tgƒtƒ ksJ ‚t dtt  tgƒtt hks J ‚t dttdƒ tgƒthks0J ‚d S )Nr}   r   rz   )rW   ri   r¥   rj   r,   rt   rt   rt   ru   Útest__simple_dens¾  s   "$r[  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sHJ ‚d S )Nrz   r}   rË  rÌ  rx   rÍ  rÃ  rÎ  FrÏ  )rÞ   rF   r-   rj   ri   r   rt   rt   rt   ru   Útest_issue_8755Ä  s   *,ÿÿÿÿÿr\  c                  C   sN  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r¢|ks¥J ‚ J ‚d S )Nr   i”ýÿÿi˜  é~   rÉ  rE  éÍ   éh   rx   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 )rx   N)rq   rÛ   rt   rt   ru   r—   ç  rÝ   z7test_issue_8828.<locals>.<listcomp>.<setcomp>.<genexpr>ré  )r’   rá  rt   rt   ru   Ú	<setcomp>ç  rj  z-test_issue_8828.<locals>.<listcomp>.<setcomp>rt   )r’   ro   rt   rt   ru   rè  ç  rž   z#test_issue_8828.<locals>.<listcomp>)ri   rj   rk   r-   rF   )rü   Úy1Úr1rT  Úy2rU  Zy3Zr3rê  Úf1Úf2Zf3r|  Úg1Úg2Zg3ró  r€  r„  r…  rh   rm   rÔ   rt   rt   ru   Útest_issue_8828Í  s,   
$ $
$$


 rh  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s7J ‚t dttƒ dtdt ƒ  ƒdt d td gksSJ ‚d S )
Nrz   r   r   r~   r>  rx   i,  rr  iÂ  )rF   r5   ri   r   rt   rt   rt   ru   Útest_issue_2840_8155ë  s   :4<ri  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   "rj  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s#J ‚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siJ ‚t td tt gttƒtdtt iks~J ‚t td d tt gttƒdt t fdt t fgksœJ ‚ttd  d } tt d dt  }tt | |gttƒƒdks¼J ‚d S )Nrx   rz   rˆ   r`  r~   )rF   ri   r   r   r-   r+   rj   rÞ   rú  rt   rt   ru   Útest_issue_11538÷  s   .22
ý*
ÿ rk  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}   rx   Tr{   r   rz   r˜   r  )ra   rb   rc   rd   re   r€   r   Ztermsr²   rÓ   Ús2Zs3Zs4Zs5rt   rt   ru   Útest_issue_12114	  s4   66ÿ &(ÿ((ÿ&(ÿ((ÿ÷rm  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s$J ‚d S rk  )rF   r   ri   rt   rt   rt   ru   Útest_inf	  s   rn  c                     sò   t dƒ‰‡fdd„tdƒD ƒ} tdƒ}tt| |ƒƒ}|d d… |dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}| d d… | dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}|| d	   |¡ ¡ ||d	   ¡ kswJ ‚d S )
Nr€   c                    s   g | ]}ˆ |ƒ‘qS rt   rt   rÛ   rh  rt   ru   rè  '	  r  z$test_issue_12448.<locals>.<listcomp>rp   zx:15rz   c                    óT   g | ]&}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS ©rˆ   r}   rx   rz   rt   rÛ   ©rc   ri   rj   rk   rt   ru   rè  ,	  ó    Lÿc                    ro  rp  rt   rÛ   rq  rt   ru   rè  0	  rr  r   )r   rø   r   r|   rÀ  rF   ZxreplacerB  )Zfunr§  rÁ  ZssymZsfunrt   )rc   r€   ri   rj   rk   ru   Útest_issue_12448%	  s&    ÿÿ ÿÿÿrs  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s1J ‚t dt dt  dt  ttgƒtthksHJ ‚t dt dt  dt  ttƒtthks^J ‚t dt dt  dt  tthƒtthksuJ ‚d S ©Nrx   r}   )rX   ri   rj   rk   rt   rt   rt   ru   Útest_denoms7	  s     ".,2ru  c                  C   s„  t dƒ\} }}}}}g | d |  ‘| | | ‘| | | ‘| | | ‘| | | ‘| | | ‘| | | ‘|  d |d  d| d  ‘|| |d  |d  |d  ‘|| |d  |d  |d  ‘|| d| d  |d  ‘|| | ‘| | | ‘|| |d  |d  |d  ‘|  d |d  |d  |d  |d  |d  ‘| d ||  |d  |d  |d  |d  ‘|| |d  |d  |d  ‘|| | ‘| | | ‘|| |d  |d  |d  ‘| d ||  |d  |d  |d  |d  ‘|  d |d  |d  |d  |d  |d  ‘| d |d  ||  |d  ‘| ||  ‘| | | ‘|| d| d  |d  ‘|| |d  |d  |d  ‘| d |d  ||  |d  ‘|  d d| d  |d  ‘| ||  ‘| | | ‘|| | ‘|| | ‘| ||  ‘| ||  ‘|  |d  ‘| d ‘}| 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s@J ‚d S )
Nzx0 x1 x2 x3 x4 x5rx   rz   r   r}   r~   r˜   r   ry   )r   r   r   r¸   r-   rF   )rû   rü   rT  rU  rV  rW  r{  Zsolsrt   rt   ru   Útest_issue_12476@	  s   J
ÿÿÿþþ
þ
þý0ý0üü
û
ûû0ú0ù ùø
øøø 	÷	÷	÷
	÷

ö

ö
ö
ö
ö
ö2"288ûrv  c                  C   s:   t dƒ} t| tdƒtdƒ  tdƒ | f| ƒg ksJ ‚d S )Nrl   ry   rx   r  )rl   rt   rt   ru   Útest_issue_13849W	  s   2rw  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kiloræ   iÀàÿÿ)Úsympy.physics.unitsry  rz  rF   ri   rj   rx  rt   rt   ru   Útest_issue_14860\	  s   0r|  c               	   C   sb  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seJ ‚t||| d|d   d | d d|d   d g|||ƒ|dtdƒ d f|dtdƒd fgks™J ‚t||d  d ||d  d fƒg ks¯J ‚d S )Nz:4r˜   r}   rx   r   r~   r>  r  )rf   rg   ra   rb   rt   rt   ru   Útest_issue_14721a	  s*   ..ýý þý0ÿÿ"ÿÿ0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s4J ‚d S )
Nri   Trò   rˆ   é‚   rx   iA  i  r  )r   rF   r-   r   rä   rt   rt   ru   Útest_issue_14779o	  s   0ÿÿÿÿr  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s6J ‚t td ttd td ddfƒtdtdiksOJ ‚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s{J ‚d S )Nrx   rz   FrX  rŽ   rˆ   r˜   iá0  iÕW i¢éÿÿr~   ræ   r  r§   rB  )rF   rj   r
   ri   r   r   )rH  rI  rt   rt   ru   Útest_issue_15307u	  s    ÿ
ÿ 
ÿ" r€  c                   C   sÔ   t td tƒdgksJ ‚t td gtƒtdiksJ ‚t ttdtd  d  tdt  ƒtƒg ks2J ‚t ttdtd  d  tdt  ƒgtƒg ksKJ ‚t ttdtd  d  tdt  ƒttdƒgtƒg kshJ ‚d S )Nrz   rx   r}   )rF   ri   r   rj   rt   rt   rt   ru   Útest_issue_15415	  s
   02>r  c                  C   sú  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sUJ ‚t td dt  d td d  dddtdƒ    ƒtdƒgksxJ ‚t tttj  dtdƒ  ƒtdƒgksŽJ ‚t td d t d ƒdgksŸJ ‚t tdt  d ƒddgks¯J ‚t td dt  tdƒ ƒddgksÃJ ‚t tttj  tddƒ ƒtddƒgksÙJ ‚t ttdƒƒ t d ƒdtdƒtdtddƒ ƒtt	   gksûJ ‚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sHJ ‚t tdƒt dtdƒ  ƒdgks\J ‚t tt d ƒdgksjJ ‚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sžJ ‚t
dƒ} t | t | d  tƒdgks³J ‚t | t d|   tƒdgksÄJ ‚t | t |  tƒdgksÓJ ‚t
ddd} t | t | d  tƒdgksêJ ‚t | t d|   tƒdgksûJ ‚d S )Nrx   rÌ   r
  r  rš   r}   )rx   rz   rˆ   ry   r   rÌ   rˆ   r~   r   rz   r-  ræ   r>  ry   rb   r˜   Tr—  )rF   r   ri   r-   r   r¸   r   r%   r   r   r   )rb   rt   rt   ru   Útest_issue_15731‰	  s4   >",F," (,D*Fÿ($D"""&r‚  c                   C   sJ   t td ttd   tƒsJ ‚t ttd  td  td  d ƒs#J ‚d S )Nrˆ   rõ  rz   rx   rþ  )rF   ri   rj   r   rt   rt   rt   ru   Útest_issue_10933©	  s   ,rƒ  c                  C   s,   t ddd} tt| t ƒ| ƒdgksJ ‚d S )Nri   Trò   r   )r   rF   r´  rj   rä   rt   rt   ru   Útest_Abs_handling®	  s    r„  c                  C   s†   t dƒ} td| d  d|   d dk| dkg| ƒtju sJ ‚t| d d| d   d	|  d  d
 dk| d dkg| gƒtju sAJ ‚d S )Nri   rx   ry   rË   r   g      ø?rz   g)\Âõ( @g=
×£p=L@éj   r}   )r   rF   r   Úfalserä   rt   rt   ru   Útest_issue_7982³	  s   4Jr‡  c                  C   sP   t dƒ\} }t| | |  | | | |  | g| |gƒ||d  |fgks&J ‚d S )Nr"  r}   rí  r/  rt   rt   ru   Útest_issue_14645»	  s   Drˆ  c                  C   sR   t dƒ\} }ttd| dk f| | dkfƒ| ƒ|td| dk f| dfƒigks'J ‚d S )Nr"  rª   rõ  T)r   rF   r.   r/  rt   rt   ru   Útest_issue_12024À	  s    ÿr‰  c                   C   s¬   t dt t t tƒtttƒtt  ƒ ttdƒƒ tttƒtt  ƒttdƒƒ gks.J ‚t ttd  td  tƒttdtdƒ dttƒ  dt t  ƒƒgksTJ ‚d S )NrÌ   r
  iõÿÿÿ)rF   ri   r   r-   r%   r   r$   r#   rt   rt   rt   ru   Útest_issue_17452Æ	  s   4
ÿPrŠ  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	  ré   r‹  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s%J ‚d S )Nri   Trò   rx   r}   r˜   )r   rF   r´  r-   rä   rt   rt   ru   Útest_issue_17650Ð	  s   BrŒ  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 s,J ‚d S )Néøÿÿÿrx   r>  r}   rˆ   rz   )ri   r   rP   re  rt   rt   ru   Útest_issue_17882Õ	  s   HrŽ  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s0J ‚t tt td  ƒtƒg ks@J ‚d S ri  )rF   r$   ri   rt   rt   rt   ru   Útest_issue_17949Ú	  r>  r  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s%J ‚t tttdƒdƒƒddgks5J ‚t tttdƒ tƒttdƒ gksHJ ‚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smJ ‚t td ttd dƒ tƒg d¢ksJ ‚d S )Nrx   rz   r~   )r`  r   r}   r   r}   )r~   r˜   rz   )rF   r   r   ri   Úpowra   rj   r5   rt   rt   rt   ru   Útest_issue_10993á	  s    * &J,r‘  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s7J ‚d S )Nr}   r˜   rx   r~   )ri   rj   r   rF   r   )rH  rI  rJ  rt   rt   ru   Útest_issue_11553ê	  s
   &,r’  c                  C   s¼  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sOJ ‚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sÉJ ‚tdttƒ ttƒ ƒtdƒgksÜJ ‚d S )Nr}   rz   ry   rˆ   rx   r~   )	r   rF   r3   ri   r5   r1   r-   r   r¸   )rl   rg   rt   rt   ru   Útest_issue_19113_19102ò	  s   "* 
þ4244
ü*r“  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sSJ ‚d S )Nrz   rˆ   ry   ræ   r}   rx   )r   r-   rF   ri   ©ra   rb   rc   rd   rt   rt   ru   Útest_issue_19509
  s   ür•  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swJ ‚d S )NzTHT HT DBH dib c0 c1 c2 c3 c4r}   )r   r$   r%   rF   )ZTHTZHTZDBHZdibZc0Úc1Úc2Úc3Zc4r€   Úrhsr…   Útermr²   rt   rt   ru   Útest_issue_20747
  s   (*ÿ"r›  c            	   	   C   sü  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sëJ ‚t t|| ƒdd }|ksüJ |ƒ‚d S )Nrx   Tr{   r   za1:6ræ   rˆ   rz   ry   r§   r   r¨   r  )rF   ri   rj   rk   r   rB   )	rÓ   Za1Za2Úa3Za4Za5r–   r²   r   rt   rt   ru   Útest_issue_27001
  s@   *Rÿÿ
ÿÿÿÿ
ÿÿÿ
ÿ
ÿ&ýH&r  c                  C   s0  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s+J ‚t|  t dt d i¡ t¡dktƒtdƒd tk ttdƒd k @ ksPJ ‚t|  t dt d i¡ t¡dktƒtd	ƒd tk ttdƒk @ kssJ ‚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}   rx   rz   r   r˜   r`  r~   rˆ   r2  )rl   rF   rÏ   ri   r   r   rh  rt   rt   ru   Útest_issue_20902#
  s
   FJFJrž  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s8J ‚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s^J ‚d S )Nra   Trò   rˆ   ry   )
r   ri   r'   r3   rj   r(   rk   r)   rF   r$   )ra   r’  Z	newsystemrt   rt   ru   Útest_issue_21034+
  s
   *:6rŸ  c                  C   sÔ   t ttd t d  td td   td  ƒ t d td   } tt t d td   }t||   t t   ||  ft||   t t   ||  fg}ttd td  td  t t tt  t gttƒ|kshJ ‚d S ri  )ra   r-   ro   rb   rc   rF   ri   rj   )rk   rl   r²   rt   rt   ru   Útest_issue_48866
  s   @<@r   c                  C   sT   t ddd\} }}}t| |t  ||t   tƒt||  ƒt|| ƒ gks(J ‚d S )Nr  Tr—  )r   rF   ri   r%   r”  rt   rt   ru   Útest_issue_6819=
  s   @r¡  c                  C   s0   t dƒ} td|  t d | ƒdt gksJ ‚d S )Nri   r}   rˆ   )r   rF   r   rä   rt   rt   ru   Útest_issue_17454B
  s   (r¢  c                  C   sB   ddt dƒ d  g} tdt t dtd  ƒ d ƒ| ksJ ‚d S )Nr2  rx   )r-   rF   ri   )rÀ   rt   rt   ru   Útest_issue_21852G
  s   ,r£  c                  C   sŒ   t  ttdt   tdt  dt   ddt    } t| tddd}|ttdt   tdt   t dt   t ddt   gksDJ ‚d S )Nr}   FrÑ  )rd   ra   rc   re   rb   rF   r  rt   rt   ru   Útest_issue_21942L
  s   6
ÿÿ
ÿr¤  c                  C   sP   t td td  t d dd} t td td  t d dd}| |ks&J ‚d S )Nry   rx   r}   F)ZcubicsTr    )r,   Zradrt   rt   ru   Útest_solver_flagsS
  s     r¥  c                  C   s’   dt d  dtd d  td   } t|  ¡ t dddt td d  tdtdƒt   td d  t dtdƒt   td d  gksGJ ‚d S )	Nrx   rz   r¨   r}   r   Fr³  r˜   )ri   rj   rk   rF   rt  r-   r   re  rt   rt   ru   Útest_issue_22768Y
  s   $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s+J ‚d S )Nrx   r~   r˜   r}   )rF   rj   r%   ri   r   rt   rt   rt   ru   Útest_issue_22717`
  s   8ÿr§  c                     s6   t d d d ‰ tˆ ƒ} t‡ fdd„| D ƒƒrJ ‚d S )Nry   r  rz   c                 3   s    | ]	}ˆ   t|¡V  qd S r   )rÏ   ri   rÛ   re  rt   ru   r—   h
  s   € z#test_issue_25176.<locals>.<genexpr>)ri   rF   r×  rß   rt   re  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sWJ ‚d S )Nr  ry   rˆ   rx   rz   r`  ræ   r2  i  iØÿÿÿé   r}   iìÿÿÿrŒ   i  iöÿÿÿrË   )r   ra   ri   rb   rc   re   r   rd   rf   r-   rK   re  rt   rt   ru   Útest_issue_10169k
  sV   Fÿÿÿÿ&ÿÿ
ÿÿÿÿÿF
ÿÿý ÿüû

6<6<úrª  c                  C   s@  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sžJ ‚d S )NzA, B, r, phiT)Ztrigrx   r˜   )r   r   r5   rl   r3   Úlhsr™  rt  rK   r1   r-   )r€  r„  rÔ   r)  re   r…   rz  rt   rt   ru   Ú*test_solve_undetermined_coeffs_issue_23927|
  s   *$Bþ$Dþ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 )Nrx   rH  )rF   r	   ri   rt   rt   rt   ru   r   Œ
  r  z"test_issue_24368.<locals>.<lambda>rl  Tr›  rx   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 rt  )rF   r	   rt   ©r€   rl  rt   ru   r   
  s   n )r_   r„   r   r*   r   rt   rt   r­  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suJ ‚d S )NrŒ   rz   r   rË   r   rx   é°   rˆ   r¬  rG  r¨   r5  éÄ   rI  r  é   r&  r  rÉ  r.  T)r   rF   r.   ÚNaNri   rt   rt   rt   ru   Útest_solve_Piecewise’
  s(   F*>">"6>"66.
îr³  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%   r8  r&   r'   r(   r)   Z#sympy.functions.elementary.integersr*   Z(sympy.functions.elementary.miscellaneousr+   r,   r-   Z$sympy.functions.elementary.piecewiser.   Z(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Z'sympy.functions.special.error_functionsr7   r8   r9   r:   Zsympy.integrals.integralsr;   Zsympy.logic.boolalgr<   r=   Zsympy.matrices.denser>   Zsympy.matricesr?   r@   Zsympy.polys.polytoolsrA   rB   Zsympy.printing.strrC   Zsympy.simplify.radsimprD   Zsympy.solvers.solversrE   rF   rG   rH   Zsympy.solversrI   rJ   rK   Zsympy.solvers.bivariaterL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   r{  rY   Zsympy.polys.rootoftoolsr[   Zsympy.testing.pytestr\   r]   r^   r_   Zsympy.core.randomr`   rÐ   rs  ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rv   r‚   r‡   r‰   rŠ   r‹   r   r´   rÁ   rÂ   rÅ   rÆ   rÇ   rÖ   r×   rÙ   rà   rá   râ   rã   rå   rç   rè   rê   rë   rí   rï   rñ   rÿ   r]  r^  ry  r}  r~  r†  rŒ  r‘  r“  r–  rš  r  rž  rŸ  r   r¨  rª  r«  r²  rµ  r¶  r·  rÙ  rÚ  rÛ  rÞ  rß  rà  rã  rï  rð  rò  rô  rù  r  r  r  r  r  r
  r  r  r  r  r  r  r  r   r!  r'  r(  r.  r0  r1  r4  r5  r9  r;  r<  r=  rA  rC  rD  rE  rF  rG  rK  rL  rN  rP  rT  rW  rZ  r[  r\  rh  ri  rj  rk  rm  rn  rs  ru  rv  rw  r|  r}  r  r€  r  r‚  rƒ  r„  r‡  rˆ  r‰  rŠ  r‹  rŒ  rŽ  r  r‘  r’  r“  r•  r›  r  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  rª  r¬  r®  r³  rt   rt   rt   ru   Ú<module>   sž    (0D
h$


7
 3('-
,



  7


+D	(,	
<

[



	

			