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    jg*¡ ã                   @   sÌ  d dl mZmZ d dlmZ d dlmZ d dlmZm	Z	m
Z
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„ Z dd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zeydd„ ƒZdd„ Zdd„ Z	dd„ Z
dd „ Zd!d"„ Zd#d$„ Zd%d&„ Zd'd(„ Zd)d*„ Zd+d,„ Zd-d.„ Zd/d0„ Zd1d2„ Zd3d4„ Zd5d6„ Zd7d8„ Zd9d:„ Zd;d<„ Zd=d>„ Zd?d@„ ZdAdB„ ZdCdD„ ZdEdF„ ZdGdH„ ZdIdJ„ Z dKdL„ Z!dMdN„ Z"dOdP„ Z#dQdR„ Z$dSdT„ Z%dUS (W  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SparseMatrix)ÚPoly)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)Ú	full_prec)rA   r   Úevalf)rc   ÚnÚoptions© rs   úX/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/solvers/tests/test_solvers.pyÚNS/   ó   ru   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 )
NÚfgé   é   é   T©Údictr   é   éþÿÿÿ)Úmapr   rg   rD   rh   )ÚfÚgÚfxÚgxrs   rs   rt   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)rD   Ú	TypeErrorÚNotImplementedError)ÚeqÚsymbolrs   rs   rt   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   rg   r_   r-   r   rh   r$   rs   rs   rs   rt   Útest_guess_polyE   s   $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   rŠ   )r‰   r-   rg   r   rh   rs   rs   rs   rt   Útest_guess_poly_cvU   s   ÿrŒ   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‰   rg   rh   r-   r   rs   rs   rs   rt   Útest_guess_rational_cv`   s
   $ÿ4r   c                   C   sœ   t ttƒd tƒsJ ‚t dttƒ t tƒsJ ‚t ttƒtt ƒ t tƒs(J ‚t dt d tƒs3J ‚t dt  d tƒs?J ‚t ttt  t tƒsLJ ‚d S )Nr}   rx   rz   é
   )r‰   r$   rg   r3   rh   r_   r`   rs   rs   rs   rt   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
gksâJ ‚ttd
 t thƒtd
igksòJ ‚tt t d
 t tgƒd
t tfgksJ ‚tt t d
 t tgddt d
t igksJ ‚tt t d
 ƒt d
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
t   d	t   ttddttd  t  d
t d
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t ƒt  t
tƒt fƒt tdƒ ttdƒ igk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   rn   c                 3   s$    | ]}t |ˆƒttƒˆ kV  qd S ©N©rD   rg   rh   )Ú.0Ú	container©ÚansÚeqsrs   rt   Ú	<genexpr>{   s   €" z"test_solve_args.<locals>.<genexpr>rŠ   rz   éÿÿÿÿT©Úimplicité*   c                   S   ó   t td td ftttƒS ©Nrz   rx   r“   rs   rs   rs   rt   Ú<lambda>‡   ó    z!test_solve_args.<locals>.<lambda>c                   S   ó   t tttƒS r’   ©rD   rg   rs   rs   rs   rt   r    ˆ   ó    ©Úexcluder   c                   S   rž   rŸ   r“   rs   rs   rs   rt   r    Œ   r¡   c                   S   r¢   r’   r£   rs   rs   rs   rt   r       r¤   r{   ©ÚsetF)r¦   Úsimplifyé   é   c                   S   s$   t ttƒttƒ ttƒ ttƒ ƒS r’   )rD   r$   rg   r5   rh   rs   rs   rs   rt   r    ³   ó   $ )r~   rx   )rx   rx   )rx   r~   ç        )r¨   Úcheck)rg   rh   ÚallÚtupleÚlistr¨   Ú	frozensetrD   r   r   r$   r-   r]   Ú
ValueErrorr_   r`   ra   re   rf   rd   r†   r#   r   ri   r   Úkeys)r‡   ÚsolÚargsrs   r–   rt   Útest_solve_argsw   sž   $
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,b2rn   rŠ   r~   )rD   rg   r   r   r¨   r   ÚOnerh   r,   r-   r   r   ÚZeroÚHalfr_   )ÚrxÚa11Úa12Úa21Úa22Úb1Úb2Úsolutionrs   rs   rt   Útest_solve_polynomial1ß   s:   "$(* 
:
ÿ.  þÿ "$ýÿÿrÄ   c                   C   s   t dtƒg ks	J ‚d S )NrŠ   r£   rs   rs   rs   rt   Útest_solve_polynomial2  ó   rÅ   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   rŠ   r«   rz   é   r   N)rD   r-   rg   r   rs   rs   rs   rt   Útest_solve_polynomial_cv_1a  s
   ""8rÈ   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 )NrŠ   r}   rx   rz   rÇ   )r¨   rD   rg   r_   r-   r   rº   r,   rs   rs   rs   rt   Útest_solve_polynomial_cv_1b  s   82rÉ   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)rD   rg   r   r»   r   r-   rs   rs   rs   rt   Útest_solve_polynomial_cv_2  s
   **ÿÿrÊ   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   rn   rŽ   é   é   ©Úexponent)rg   rD   Úsubsrq   ÚtnÚfuncrY   rF   ©r€   ÚsÚrÚresrs   rs   rt   Útest_quintics_1"  s   ,,&	 ÿrÙ   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   rn   rª   FrÍ   r   rz   rx   rŽ   rÎ   r‘   r}   rŠ   )rg   rD   rÒ   rq   rÓ   rÔ   rY   rÕ   rs   rs   rt   Útest_quintics_29  s    ,*,,,,,ûrÚ   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}   )rg   r   rD   ©rh   rs   rs   rt   Útest_quintics_3M  s   *rÜ   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
isinstancerY   ©r”   Úirs   rs   rt   r™   U  ó   € z&test_highorder_poly.<locals>.<genexpr>)rD   rg   r¯   Úlen©rµ   rs   rs   rt   Útest_highorder_polyR  s   &rã   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)rD   rg   rh   r-   rs   rs   rs   rt   Útest_solve_rationalX  s   <rä   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)rD   r    rg   r   rs   rs   rs   rt   Útest_solve_conjugate]  s   &rå   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{   )rD   rg   rh   r$   r-   rs   rs   rs   rt   Útest_solve_nonlinearb  s   26ÿræ   c                  C   sl   t dƒ} tt| d d| d d   dd| d d   ƒ| ƒg ks"J ‚tt| d|   d|  ƒ| ƒg ks4J ‚d S )Nrg   rx   r}   rŠ   )r   rD   r   ©rg   rs   rs   rt   Útest_issue_8666h  s   <(rè   c                   C   s:   t ddtd  dt   d tƒtddƒtjgksJ ‚d S )NrŠ   rx   é   r   )rD   rg   r   r   r»   rs   rs   rs   rt   Útest_issue_7228n  s   :rê   c                   C   s0   t ttd ƒttd ƒ tƒtdƒgksJ ‚d S )Nrz   rŽ   )rD   r%   rg   r-   rs   rs   rs   rt   Útest_issue_7190r  ó   0rë   c                  C   s<   t dƒ} | t| d d ƒ }| | ¡}t|| ƒg ksJ ‚d S )Nrg   rx   r}   )r   r-   r   rD   )rg   r€   Úf_diffrs   rs   rt   Útest_issue_21004v  s   
rî   c                  C   st   t dƒ} ttt| t| dƒ| dkB fƒdƒƒ}|dgksJ ‚ttt| t| dƒ| dkB fƒdƒ| dd}|du s8J ‚d S )Nrg   r   r}   râ   T)r   rD   r   r.   rO   )rg   r×   rs   rs   rt   Útest_issue_24650}  s
   $*rï   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   r   r‘   rn   r   r~   )rš   r   r}   r   r   )r   rD   r>   rG   )rg   rh   ri   rj   rq   ÚMrs   rs   rt   Útest_linear_system…  s   222<"þ*ÿ>rñ   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      $@g     à…@)r}   r}   r}   g      Y@)r   rò   g      @g      i@)g      Àr   r   r   r   g      NÀg      d@)r>   rG   rg   rh   ri   )rð   rs   rs   rt   Útest_linear_system_xfail™  s   ý&ró   c                  C   sš   t dƒ} t| ddƒ| ddƒ | ddƒ | ddƒ | ddƒ | ddƒ g| ddƒ| ddƒ| ddƒ| ddƒƒ| ddƒ| ddƒ | ddƒ| ddƒ iksKJ ‚d S )Nr_   r   r}   )r   rD   ©r_   rs   rs   rt   Útest_linear_system_function¤  s   > ÿ&ÿrõ   c                  C   s2   dd„ } t ddƒD ]}| |ƒ\}}t||ƒ q	d S )Nc           
         sÔ   d|  d }t ddd\‰ }}t d | ¡dd}t d | ¡dd}t d |d ¡dd}t‡ fd	d
„t|ƒD ƒƒ}g }t| ƒD ]&}	| | ˆ |	¡ ˆ |i¡||	  ¡ | | ˆ |	¡ ˆ |i¡||	  ¡ q?||fS )Nrx   r}   z	x, x0, x1T©Úrealzy0_:{}zy1_:{}zc_:{}c                 3   s     | ]\}}|ˆ |  V  qd S r’   rs   )r”   ÚoÚcoeffrç   rs   rt   r™   µ  s   € zLtest_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqs.<locals>.<genexpr>)r   ÚformatÚsumÚ	enumerateÚrangeÚappendr   rÒ   )
ÚwyÚorderÚx0Úx1Úy0sÚy1sra   Úexprr˜   rß   rs   rç   rt   Ú_mk_eqs¬  s   $&z9test_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqsr}   ré   )rý   rD   )r  rq   r˜   ra   rs   rs   rt   Ú(test_linear_system_symbols_doesnt_hang_1ª  s
   þr  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$ƒd “|td%ƒ d “|td&ƒ d “|td'ƒ d( “|td)ƒd( “|td*ƒ d “|td+ƒd, “|td-ƒ d “|td.ƒd  “|td/ƒ d |td0ƒd i¥}t| t |d1 ƒ ƒ}t||ƒ|ksüJ ‚td2ƒ}t||  t |d1 ƒ ƒ}t||ƒ|ksJ ‚d S )3N)éB   é   é'   é2   éX   é(   é%   é`   r«   éA   é   é   r  éH   r«   é   rÌ   r  é   éL   )rŽ   é]   é"   éb   é;   é,   éC   éJ   r  é^   éG   é=   é<   é   r‘   rx   é9   ré   é   éN   )r  é[   r#  é   é@   r  r	  é5   éM   r  éU   é:   éW   r
  r
  rÏ   é$   r  r&  rz   )r  éF   rn   r)  éD   é+   éV   éS   éQ   r  é   é.   r  é   r  r5  r%  r
  é?   r‘   )éE   r  r  é   r  r  r7  r'  r  r  r6  éY   é>   r  é   é&   é   rÎ   rª   r4  )r  é   r  r  r  é-   r  r  r  r  r  éc   éa   éR   ré   r6  rB  r#  r0  é#   )r,  r?  rA  r  rŽ   r(  é	   r  éZ   rD  r7  é)   r1  r4  rA  r3  r@  r  r	  r
  )r   r:  r/  r0  r‘   é!   r(  r4  r3  rn   r2  éK   r2  r7  r*  r  r<  r  rÎ   r	  )rÏ   ré   rx   r  r  é4   r  ry   é    é3   r  r.  éO   r  r5  r*  r$  é   rI  r'  )r  r  r=  r+  r4  r
  r8  r  r  rª   r«   é1   r  r  r>  r'  rz   r  r   rM  )r$  rD  éP   rP  rO  r+  r}   r  rx   r  é6   rD  rO  é/   rR  rF  rE  r   rB  r  )rn   rP  rD  r&  r  r#  rA  r5  rA  rC  rn   r  é0   rK  r  r	  r<  rR  rC  r  )r<  r"  éI   r)  rK  r2  r  r>  r   r  é\   r>  rC  r/  r  r$  rO  rG  r  rA  )rx   rL  r"  r	  r  r  r5  r  ry   rH  rC  r  r  r'  r  rA  r5  r  r9  r  )r  é8   r}   r$  rN  r  rN  r<  r  r  rA  rS  rz   r}   rL  r  r  rE  éT   rL  )rI  rn   r-  rN  r  rF  é   r8  r	  r  r6  r  r  rÎ   r$  r  rX  r&  r  r}   )rC  r?  rª   rK  r}   rx   r  rY  rK  r  r  rD  rH  rU  rM  rN  r'  rz   rD  r  )r  r  rK  rŽ   rŽ   r  rW  r%  rD  ry   r$  rT  r}   rO  r«   r?  r  r  r2  rK  )r>  r;  r3  r1  r$  rK  rG  r*  r#  r   r  rÎ   r4  r  rT  r  r  r,  rY  rz   zx:19l	   ³fœX·j"Ìbµ!SBs= l	   Ì0e7HPÈég%Oï0 l   B>é tsypYÎ/l   s LYÀr%ú9És;Ll   eAnA²&d%â$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}   rh   )r>   r   r   r±   rD   r   )rð   Úsymsr  r  Úx2Úx3Úx4Úx5Úx6Úx7Úx8Úx9Úx10Úx11Úx12Úx13Úx14Úx15Úx16Úx17Úx18rµ   r˜   rh   rs   rs   rt   Ú(test_linear_system_symbols_doesnt_hang_2Ç  s‚   í2ÿþýüûúùø	÷
öõôóòñðïírm  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 )Nrq   )r}   rx   r   r}   r}   rz   rx   rŠ   rš   r   r?  rª   r‘   )r   r>   rH   rg   rh   ri   )rq   rð   rs   rs   rt   Útest_linear_systemLUþ  s   *"þrn  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   ©r_   r`   rz   rx   rŠ   r«   ry   iíÿÿÿré   éüÿÿÿc                 3   ó(    | ]}ˆ   t|¡jd ddkV  qdS ©T)Úchopr   N©rÒ   rg   rq   ©r”   r_   ©r‡   rs   rt   r™   +  ó   €& z,test_solve_transcendental.<locals>.<genexpr>r}   r‘   rÏ   rF  ia	  rÎ   rŽ   r€   c                      s   t ˆ ttƒˆ ddƒ tƒS ©Nr}   rx   r“   rs   ©r€   rs   rt   r    g  r¡   z+test_solve_transcendental.<locals>.<lambda>c                      s   t ˆ ttƒˆ dt dƒ tƒS ©Nrx   r“   rs   ry  rs   rt   r    h  ó    c                      s   t ˆ ttƒˆ dt ƒ tƒS ©Nr}   r“   rs   ry  rs   rt   r    i  s    c                      s   t ˆ ttƒˆ dƒ tƒS r|  r“   rs   ry  rs   rt   r    j  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   )rD   r(   rg   r'   rs   rs   rs   rt   r    p  rì   c                   S   s   t td t t d tƒS ©Nrx   rz   r“   rs   rs   rs   rt   r    t  r¡   za, bTF)r÷   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.abcr_   r`   rD   r$   rg   r%   r¨   r3   rh   r/   r   r   r5   r-   r   r#   r   r   rá   r¯   Úexpandri   r0   r   r]   r†   r³   r   ÚstrÚis_Rationalr»   )r_   r`   r—   Úresultr  r  r\  r]  r^  r_  r`  ra  rb  rc  rd  Úyirµ   rs   )r‡   r€   rt   Útest_solve_transcendental  sÆ    80<&þþ""þ
ú"	$"(0 (
ÿ4@
*<"(

$ü>F,&þ.F2F.*."$&(@B*2:"&""
ÿ.* ,,8<4rŠ  c                  C   sŠ  t dƒ} tdƒ| ƒ}tdƒ| ƒ}tdƒ\}}}}}}t|| ||  | || ||  | g||ƒ}	|	||| ||  || ||   ||| ||  || ||   iksXJ ‚t|d |ƒdgksdJ ‚td| d |ƒtddƒgksuJ ‚t|| | ¡ || | ¡  | || | ¡ || | ¡  | g| | ¡| | ¡ƒ}	|	| | ¡|| ||  || ||   | | ¡|| ||  || ||   iksËJ ‚t| | ¡d | | ¡ƒdgksÝJ ‚td| | ¡ d | | ¡ƒtddƒgksôJ ‚d| d d| d h}
t|
||hƒ|tddƒ|diksJ ‚t dƒ}td	ƒ}|d ||ƒd  d|  d }t| |¡t||ƒ|ƒƒ| d ||ƒ gksEJ ‚t dƒ}tdƒ| ƒ}t|| || | ¡  | || || | ¡  | g|| | ¡ƒ}	|	| | ¡|| ||  || ||   ||| ||  || ||   iksšJ ‚t dƒ}td	ƒ}t||ƒ |¡||ƒ |d¡ d ||ƒ |¡||ƒ |d¡ g||ƒ |¡||ƒ |d¡ƒ}	|	||ƒ |d¡tdƒd ||ƒ |¡tdƒd iksïJ ‚t||ƒ |d¡||ƒ |d¡ d d||ƒ |d¡ ||ƒ |d¡ d||ƒ |d¡ g||ƒ |d¡||ƒ |d¡ƒ}	|	||ƒ |d¡d
||ƒ |d¡diksCJ ‚d S )Nrj   rg   rh   r¸   r}   rz   rx   rŠ   r€   r   )r   r   r   rD   r   r   r   )rj   rg   rh   r½   r¾   r¿   rÀ   rÁ   rÂ   ÚsolnÚeqnsr€   ÚFrs   rs   rt   Ú$test_solve_for_functions_derivativesŽ  sn   0  
þ",ÿÿÿ(&
ÿ$.& 4 ÿÿ
ÿ( ÿ@ÿ<6ÿÿÿ2rŽ  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   rŠ   r}   )r   rg   r   rD   )r€   r  rc   rs   rs   rt   Útest_issue_3725Á  s    
Br  c               	   C   st  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 ‚d S )
Núa b c drx   )r   rx   r   r   )r}   rx   rz   rŠ   r}   rš   rz   r~   r   )r   r>   rD   r   r   )r_   r`   ra   rb   ÚAÚBÚCrs   rs   rt   Útest_issue_3870È  s   8:::>B<BL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   rš   c                   S   s   t ttdƒdƒS r~  )rE   r   rg   rs   rs   rs   rt   r    õ  ó    z#test_solve_linear.<locals>.<lambda>)
r   rE   rg   rh   r3   r5   r   r$   r]   r³   )r•  r‡   rs   rs   rt   Útest_solve_linearÛ  s6   .(.&&""ÿ2*4*&"$rš  c                  C   sX  t ttd  ttd   tt  dt t  t d tttgtƒtdtdtdiks+J ‚t tt ttd   dt d td t   ttgtƒtdtdiksOJ ‚t td t td  td t td   td t t  td d t t  td d  td  tttgtƒtdtdtdiksJ ‚ttt ttt  } }}t|  t|  t|  |  d|  d|  }tttf}ttf}t ||ƒtdtdtdiksÌJ ‚t |||ƒtdtdtdiksÜJ ‚t ||g|¢R Ž tdtdtdiksïJ ‚t tt t d tgƒg ksÿJ ‚t td t dt  tgƒtditdigksJ ‚t dtgƒg ks#J ‚t dtgdd	g ks0J ‚t dtgdd
g i fks?J ‚t dtgƒg ksJJ ‚tt dt  t d }tth}t ||tƒtdtdiksiJ ‚t ||tdd
ttgdhfks{J ‚t ttt ƒtdt ƒ tfƒd u sJ ‚t tt tt  dt  ttfƒtdt iksªJ ‚d S )Nrx   r}   r~   rš   rz   rŠ   r   Tr{   r§   )rx   rz   )rI   r_   rg   r`   ra   rh   r5   )ÚXÚYÚZr‡   Úcoeffsr[  ÚabeqrÖ   rs   rs   rt   Útest_solve_undetermined_coeffsø  sj   <ÿþÿÿ
ÿ&ÿÿ
ÿÿ
ýü,

ÿ

ÿ
ÿ ÿ$*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 )Nrg   r}   rx   r   rš   Trö   rz   r‘   ry   F)r   r<   r   rº   r   rD   r   r   r=   r-   r   r5   r»   r   r   r¹   r   )rg   rµ   Úsystemrs   rs   rt   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   rš   rŠ   rÏ   c                 3   rq  rr  rt  ru  rv  rs   rt   r™   T  rw  z"test_issue_4793.<locals>.<genexpr>Tr§   c                   S   s   t ttƒttƒ tƒS r’   )rD   r%   rg   r$   rs   rs   rs   rt   r    [  ó    z!test_issue_4793.<locals>.<lambda>c                   S   s   t dt ttƒ d ƒS r  )rD   rg   r$   rs   rs   rs   rt   r    \  r}  )rD   rg   r-   r$   rh   r%   r5   r3   rá   r¯   ri   r]   r†   ©r—   rs   rv  rt   Útest_issue_4793G  s,   .. $ 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}   r_   r   rx   rÏ   rY  r€   ry   rF  i´~ûÿi©æ  rŠ   rš   r7  rp  rf   T©Úpositive)rD   r-   rg   r   r¨   r   r   rº   r   r   r,   r@   r$   r%   rh   ri   ÚExp1r   )r_   r€   r   rf   rs   rs   rt   Útest_PR1964_  sF   2$0:,<(((&ý
ÿ  
ÿ :
ÿ<ÿ.
ÿDDþ&r©  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 )Nrg   Trö   rx   r}   rq   ©Úintegerr§  r¦  rh   ry   r   r‘   rn   r{   zx y z)r   rD   r-   r$   r   )rg   rq   rh   ri   rs   rs   rt   Útest_issue_5197Œ  s   ,44>Tr¬  c                   C   s¸   t ttttt   tddƒttƒtjttƒ hksJ ‚t ttttt   tddƒttƒttƒ hks6J ‚tddt d  dtd  d fƒg ksLJ ‚tddt d  ƒg ksZJ ‚d S )NFrÍ   Tr}   rx   rz   )r¨   rD   rg   rh   r-   r   rº   rs   rs   rs   rt   Útest_checkingž  s   ÿÿ4, r­  c               	   C   sz  t ttd d ƒd ƒtdƒtdƒ gtdƒ tdƒgfv s J ‚t dttd t ƒ d td d  tƒtttdtt tdƒ  ƒ ƒ tttdtt tdƒ  ƒ ƒgksXJ ‚tdƒ\} }t	dƒ}t | |td   t|tƒ ƒ |tƒƒttd | td  |  ƒgks‡J ‚t
dƒ}tj}t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv sÅJ ‚t t|d	 td  ƒ| tƒtd
|d	  ƒ td
|d	  ƒgtd
|d	  ƒtd
|d	  ƒ gfv søJ ‚t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv s0J ‚t |d d t|t ƒt|t ƒ  tƒt d|  gksPJ ‚t dt|t ƒt|t ƒ  tƒtdƒ| gkskJ ‚tt dt|t ƒt|t ƒd   tƒƒtdtdƒ ƒ| ttdƒ d ƒ| ttdƒ d ƒ| tdtdƒ ƒ| hks«J ‚t ttƒd ƒtdƒgks»J ‚d S )Nrx   r}   ry   rn   zC1 C2r€   r_   rŠ   r   rš   rz   r~   )rD   r-   rg   r$   rh   r%   r   r   r   r   r   r   r¨  r5   r3   r(   r'   r¨   r1   r6   )ÚC1ÚC2r€   r_   r   rs   rs   rt   Útest_issue_4671_4463_4467¨  s>   &
ÿ(>
ÿJ$$
þ  
þ$$þ@6(&&ÿ
ÿ$r°  c               	   C   sH  t dƒ\} }tt| td  td  t|ƒtt  gttgƒƒt| t|ƒd  ƒ dt| t|ƒd  ƒ t|ƒ ft| t|ƒd  ƒt| t|ƒd  ƒt|ƒ fhksTJ ‚tttƒt	tƒ dt d gttgƒt
t	tddƒƒƒtddƒfgksxJ ‚tttƒt	tƒ dttƒ d gttgƒt
t	t
dƒƒ ƒt
dƒ fgksžJ ‚ttttƒt	tƒ td d gttgƒƒt
t	dƒ ƒtdƒ ft
t	dƒƒtdƒfhksËJ ‚ttƒd t	tƒ td  dttƒ d g}t|ddttgt
dƒ ttdt ƒ t	t
dƒƒ ƒft
dƒ ttdt ƒ t	t
dƒƒ ƒ fhfksJ ‚t|ttddttgtttdt ƒ t	tƒ ƒftttdt ƒ t	tƒ ƒ fhfksEJ ‚tt|ttƒƒt
ttd  t	t
dƒƒ ƒ ƒt
dƒ ft
td  t	t
dƒƒ ƒd t
dƒ fhksyJ ‚tt|ttƒƒt
dƒ ttdt ƒ t	t
dƒƒ ƒ ft
dƒ ttdt ƒ t	t
dƒƒ ƒfhks­J ‚ttƒd t	tƒ t dttƒ d g}t|ddttgt
dƒ tdt ƒ t	t
dƒƒ fhfksáJ ‚t|ttddttgttdt ƒ t	tƒ fhfksþJ ‚tt|ttƒƒt
tt t	t
dƒƒ ƒ ƒt
dƒ ft
t t	t
dƒƒ ƒd t
dƒ fhks.J ‚t|ttƒtdt ƒ t	t
dƒƒ t
dƒ fgksJJ ‚tttd td  ƒtd	ƒ tt d fddttgtjtdƒftdƒtjfhfkswJ ‚ttttd td  ƒtd	ƒ tt d fttƒƒtjtdƒftdƒtjfhks¢J ‚d S )
Nzr,trx   rš   r}   rz   rŠ   Tr§   rŽ   )r   r¨   rD   rg   rh   r6   r-   r3   r$   r5   r%   r   r   ri   r¹   )r×   rj   r˜   rs   rs   rt   Útest_issue_5132Å  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manualÚminimal©r   rh   rg   rá   rD   ©ÚlamÚa0Úconcr_   r`   r˜   Úsymrs   rs   rt   Útest_issue_5335ñ  s   ."
þ
r½  Ú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 )Nr²  r³  r´  rx   r}   F©Úrationalr·  r¸  rs   rs   rt   Ú_test_issue_5335_floatþ  s   ."
þ
rÁ  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   rŠ   )r¨   rD   rg   rh   r-   rs   rs   rs   rt   Útest_issue_5767  s    ÿrÂ  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)r÷   r§  zSigma_f, Sigma_a, nurg   rx   rz   iÁ‡ i'  r‘   r}   ré   rÏ   éd   iá  )r   r   r   r-   )ÚDrm   ÚHÚB_gÚVÚD_cÚSigma_fÚSigma_aÚnurg   r‡   Úexpectedrs   rs   rt   Ú_make_example_24609  s   >"ÿFþÿ
rÍ  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›+¡†›„=)rÍ  rD   rq   Úabs)r‡   rÌ  rg   Ú	solapproxrs   rs   rt   Útest_issue_24609  s   rÑ  c                  C   s(   t ƒ \} }}tt| |ƒƒ|gksJ ‚d S r’   )rÍ  rá   rD   )r‡   rÌ  rg   rs   rs   rt   Útest_issue_24609_xfail%  s   rÒ  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   rŠ   )r¨   rD   rg   rh   r   r¹   r-   rs   rs   rs   rt   Útest_polysys:  s   ,"ÿÿ(,ÿÿ
ÿÿrÓ  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   )rN   r-   rg   rs   rs   rs   rt   r    F  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   )rN   r-   rg   r   rh   rs   rs   rs   rt   r    H  ó   *rÖ   )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boolr…  )Úrvr—   rc   r_   )Ús_checkrs   rt   r®   O  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ziprá   rÒ   r…  r†  )rÙ  r—   rb   Úreps©rÖ   rs   rt   rÚ  W  s   66&ÿztest_unrad1.<locals>.s_checkr}   rz   rx   r‘   ry   r(  r~   r«   rF  rŠ   r5  ix  iè  ià  i  ré   iÜ  iæ	  i¼  é©   rH  r  éè   é    FrÍ   z32*sqrt(x)*(x + 1)**(1/3) + x - 4*y + (x + 1)**(2/3)r'  rÏ   iúÿÿÿrš   r   rª   rP  rŽ   rÇ   r7  r  c                   S   s(   t ttƒttdƒ ttd dƒ d ƒS )Nrz   r}   ry   rx   )rD   r-   rg   r,   rs   rs   rs   rt   r    ¿  s   (c                   S   s   t tdƒ ttƒt  ƒS rz  )rD   r-   r'   rg   rs   rs   rs   rt   r    Â  r¡   r	  r@  éÔ   éÀ   rW  i	=  iÈ£ im i { i  r  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   rŠ   ry   r}   )rN   r,   rg   rÒ   rs   rs   rs   rt   r    Ü  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
  rQ  r=  rO  T)Ú_reverserY  rU  é»   é  éä   r;  r"  rL  rn   z!(x+y)**(2*y/3) + (x+y)**(1/3) + 1é þÿÿé@  é˜  é®  ©Ú_unradz9-x + (7*y/8 - (27*x/2 + 27*sqrt(x**2)/2)**(1/3)/3)**3 - 1r:  i   iW  i   iÀ  rT  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’   )r…  Úis_zeroru  r¤  rs   rt   r™   A  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™   rM  éf   iT  i06  r?  i`2 i2  iìy  ix… i,ð  i*  c                   S   s&   t ttdƒttdƒ ttt dƒ ƒS )Nrz   ry   )rN   r,   rg   rh   rs   rs   rs   rt   r    g  s   & )!r]   r†   r   r   rN   r-   rg   r,   r   r_   r`   ra   rh   rb   r   r¹   r¨   rD   rº   r   rP   r   rj   r'   r»   rá   ru   r   ÚreversedrÒ   r   Úanyr$   )	r®   r‡   ri   rf   rc   r  r›  Úxirœ  rs   )r—   rÖ   rÚ  rt   Útest_unrad1D  s0  ÿ
ÿ"ÿÿÿ$ÿÿ$ÿ4:
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ÿ
ÿ
ÿÿÿÿ
ÿ2:
ÿ
ÿ
ÿ
ÿ
ÿ
þþþþ
ÿ
ÿ
ÿ,("ÿ,40Fÿ*ÿ
ÿþþþý"ÿÿÿý
ÿ:
ÿ"Bÿÿÿÿþþþ
ÿÿVP
ÿ>$4r÷  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}   rŠ   rx   )r-   rg   rD   r   r»   rv  rs   rs   rt   Útest_unrad_slowz  s   Drø  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   rš   rŠ   ré   rŽ   r   )rD   r,   rg   r   rY   rs   rs   rs   rt   Útest_unrad_fail‚  s   6&Bÿrù  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=r  ©Ú	numericalrV  ry   r‚  c                      s
   t ˆ dƒS r|  ©rO   rs   rç   rs   rt   r    ¤  s   
 ztest_checksol.<locals>.<lambda>c                      s   t g ˆ dƒS r|  rü  rs   rç   rs   rt   r    ¥  r¤   )r   r-   r6   rO   r   r   r@   r$   r%   r   r   r]   r³   )rh   r×   rj   r‡   Údict_var_solnrs   rç   rt   Útest_checksol‹  s6   &ÿ    ($$ ,4rþ  c                   C   s¢   t td ƒdtfksJ ‚t dƒdksJ ‚t tdt ƒd tƒdtdƒ tfks)J ‚t tdt tt  ƒd tƒtd tdƒ tfksDJ ‚t ttƒtdfksOJ ‚d S )Nrx   )rx   r   r}   rz   r   )rM   rg   r$   r%   r_   rs   rs   rs   rt   Útest__invert¨  s
   *6rÿ  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   rŠ   )rD   r_   rg   r%   r$   r#   rs   rs   rs   rt   Útest_issue_4463°  s   2&2r   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)rµ  r®   r©   )r   rá   rD   )r_   r`   ra   rb   rc   r€   r   re   rß   Újrd   Úlrl   rq   rø   rf   rk   r×   r[  r˜   rs   rs   rt   Útest_issue_5114_solvers¶  s   ,****û"r  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   rª   rp  ré   rŠ   r‘   r	  TF)rµ  r®   r|   ©rµ  r®   c                    s"   g | ]‰ t ‡ fd d„ˆD ƒƒ‘qS )c                    s   g | ]}ˆ   ||¡‘qS rs   )ÚgetrÞ   rô   rs   rt   Ú
<listcomp>ç  r}  z.test_issue_5849.<locals>.<listcomp>.<listcomp>©r°   )r”   )Úvrô   rt   r  æ  s    ÿz#test_issue_5849.<locals>.<listcomp>rµ  c                    s   g | ]	}|  ˆ d  ¡‘qS ©r   )rÒ   )r”   Úeir¤  rs   rt   r  í  s
    ÿÿr   ©r   rD   ©ÚI1ÚI2ÚI3ÚI4ÚI5ÚI6ÚdI1ÚdI4ÚdQ2ÚdQ4ÚQ2ÚQ4rc   rs   )r—   r
  rt   Útest_issue_5849Æ  s@   


*÷$ù	" ÿ
ÿÿr  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.
    r  r  r~   rx   rz   rª   Nr  r  rs   rs   rt   Útest_issue_5849_matrixñ  s   



*÷$r  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   rF  rŠ   rz   r'  r?  rÎ   r   r~   Tr{   )r   r   rD   )r_   r`   ra   rb   r€   r   rd   ÚunknownsÚ	equationsÚanswerÚgotrs   rs   rt   Útest_issue_21882  s"   <" ÷$&ýr!  c                     sŽ  t tdƒ\‰ } }tdƒ}tˆ tƒtƒ}t| |ƒ|ƒ}tˆ tƒˆ tƒ t¡ ˆ tƒƒ| gks0J ‚tˆ tƒd ˆ tƒƒdgks@J ‚tˆ tƒdˆ tƒ t¡  ˆ tƒƒd| gksYJ ‚tˆ tƒdˆ tƒ t¡  gˆ tƒƒˆ tƒd| iksvJ ‚tˆ tƒdˆ tƒ t¡  ˆ tƒd t d gˆ tƒtƒd| d|d  d fgks¢J ‚tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒdd||ƒ| |ƒgtˆ |ƒd | |ƒd  | ƒ ˆ |ƒ | |ƒftˆ |ƒd | |ƒd  | ƒˆ |ƒ | |ƒfhfks2J tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒddƒ‚ˆ tƒ td¡ˆ tƒ| tƒ  d| tƒd  gˆ tƒ| tƒg}t|d	diŽd
 tdƒ tdƒftdƒtdƒ fhksoJ ‚ˆ tƒd | tƒ dˆ tƒ t¡  | tƒd d g}t|ˆ tƒ| tƒddˆ tƒ| tƒgtd| d ƒ t	dƒftd| d ƒt	dƒftd| d ƒ t	dƒ ftd| d ƒt	dƒ fhfksÓJ ‚t
t‡ fdd„ƒ tˆ tƒˆ tƒ t¡ tgdˆ tƒtˆ tƒtƒ d
fksüJ ‚tˆ tƒttttfƒ tgdˆ tƒttttfƒ d
fksJ ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ d
fks@J ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ fkscJ ‚ttˆ tƒ|  ˆ tƒd
 |  tgdtd
| fksJ ‚tttdt tƒ ƒtdfks“J ‚tttttƒ tgdtdfks¦J ‚tttttƒ d tgdtdtd
  fks¿J ‚tttttƒd  ttƒƒƒtt ƒ tt ƒhksÜJ ‚ttttƒ tddttƒ gksðJ ‚tttƒttƒ tddg ksJ ‚ttttƒ tddttƒgksJ ‚ttd t d tddtd  d gks-J ‚ttd t d td ddt d gksEJ ‚d S )NÚfghr_   rz   rx   rŠ   rF  Tr§   r¨   r}   c                      s$   t ˆ tƒˆ tƒ t¡ ˆ tƒgdS )Nr—  )rE   rg   r   rs   ry  rs   rt   r    K  r¬   z!test_issue_5901.<locals>.<lambda>r—  r~   r   r›   )r   r   r   r   rg   rD   r   rh   r-   r   r]   r³   rE   r;   r¨   r$   r3   r5   )r   re   r_   rÄ  ÚGr¶   r˜   rs   ry  rt   Útest_issue_5901&  s®   ÿÿ"ÿ$ÿ8ÿ@ÿ0.þþ@ÿü>"
ÿ6ü
ÿÿ
ÿ
ÿ"
ÿ"
ÿ(

ÿ
ÿ
ÿ
ÿ
ÿ

ÿ$
ÿ
ÿ
ÿr$  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¿  rE  rŽ   Fc                 s   ó    | ]}|j V  qd S r’   ©Ú	is_Numberru  rs   rs   rt   r™   n  ó   € z"test_issue_5912.<locals>.<genexpr>c                 s   r&  r’   r'  ru  rs   rs   rt   r™   p  r)  )r¨   rD   rg   r   r»   r-   rá   r¯   r¤  rs   rs   rt   Útest_issue_5912j  s   $ÿ"&r*  c                  C   s†  dd„ } t td ddd jsJ ‚t td ddd jsJ ‚t ttj ddd js,J ‚t td d dd js9J ‚t ttj d dd jsGJ ‚| tdd	t  ƒd
dt  ƒsXJ ‚ttt	fD ]"}t|dd	t  gƒƒ}t
|ƒ|u r}| t|ƒd d
dt  ƒsJ ‚q]ttd	t dd	t  giƒ ¡ ƒd \}}| |d	t ƒr§| |d d
dt  ƒs©J ‚| ttd	t ƒƒtdt ƒƒsºJ ‚| tdtd	  ƒdtd	  ƒsËJ ‚| tdtd	  dddtd  ƒsÞJ ‚| ttd	t ƒƒtdt ƒƒsïJ ‚| ttd ƒtd ƒsüJ ‚| ttd d	t  ttddƒƒ d ƒtd dt  d ƒsJ ‚dt t t }t dt | d dt | d t| d fƒg ksAJ ‚d S )Nc                 S   s   t |  t¡ƒt | t¡ƒkS r’   )rá   rÛ  r   ©Úe1Úe2rs   rs   rt   Útestt  s   z!test_float_handling.<locals>.testr  Tr¿  r   Fr}   rx   ç      ð?g       @rz   g      @rÐ   rŠ   g!ÌÈ,‹ÿ?rÃ  gffffffæ?g333333ã?gš™™™™™É?g333333Ó?r%  )rD   rg   r‡  Úis_Floatr   r»   rF   r±   r°   r¨   ÚtypeÚitemsr3   r$   r   ra   ri   rj   )r.  Úcontainr—   rd   r
  Útotrs   rs   rt   Útest_float_handlings  s,   ",*(""&"&
ÿ<r5  c                  C   s*   t ddd} t| d d ƒdgksJ ‚d S )Nrg   Tr¦  rx   r}   r  rç   rs   rs   rt   Útest_check_assumptions  ó   r6  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}   r   rŠ   rx   )rD   r)   rg   r   r   r   rs   rs   rs   rt   Útest_issue_6056’  s   (8ÿ"8ÿr8  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   TFrú  )rg   r$   r#   r%   rO   rv  rs   rs   rt   Útest_issue_5673š  s   &r9  c            
      C   s¶  t dƒ\} }}}}}}}t ddd}|| | |d| | d|     |d| d|   ||  || | || | d|     ||   | | g}	t|	|| |  d||||  | d d	  ||  |  |||d	| |||  |   |||  | | d
|  |||  |   i|d|d|d|digks–J ‚t|	|||gd||||d	 |d	  t|d|  ||  ƒd	  | |d
|  t|d	 d| |  d|d	   ƒ d	| | |  ||||  | i||||d	 |d	  t|d|  ||  ƒd	  | |d
|  t|d	 d| |  d|d	   ƒ d	| | |  ||||  | ig||||d	 ||  |d	  |d	|   |||| d	  ||d	|    | ||| |d	|    igfv sYJ ‚d S )Nz$R, C, Ri, Vout, V1, Vminus, Vplus, sÚRfTr¦  r~   r}   rš   r¥   rx   rz   r   ry   r‘   ©r   rD   r-   )
rm   r“  ÚRiÚVoutÚV1ÚVminusÚVplusrÖ   r:  r˜   rs   rs   rt   Útest_exclude   sL   ÿ"(ý$(üü
ú,@ü,@üû$ üörA  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   rŠ   rz   rx   rÏ   ÚZZ)Údomain)rg   r   r¨   rD   r@   Ú	all_rootsrÞ  rs   rs   rt   Útest_high_order_rootsÈ  s   *,rE  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 r  rs   )r”   rg   rs   rs   rt   r  Ó  r}  z>test_minsolve_linear_system.<locals>.count.<locals>.<listcomp>)rá   Úvalues)Údicrs   rs   rt   ÚcountÒ  rÆ   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   rš   rš   r   r   )rš   rš   r   r   rš   r   r   r   r   r   r}   r}   r   r}   )r}   r   r}   r}   r   r}   r}   r   r   r}   rš   r   rš   r   )rš   r   rš   r   r   rš   r   r   r   r   r}   r   r}   r}   )rš   r   r   rš   r   r   rš   r   r   r   rš   r   r   rš   )r   r}   r}   r}   r   r   r   r}   r}   r}   r   rš   rš   r   )r   rš   rš   r   r   r   r   rš   r   r   r   r}   r}   r}   )r   rš   r   rš   r   r   r   r   rš   r   r   rš   r   rš   )r   r   rš   rš   r   r   r   r   r   rš   r   r   rš   rš   )r   r   r   r   r}   r}   r}   r}   r}   r}   r   r   r   r   )r   r   r   r   rš   rš   r   rš   r   r   r   r   r   r   zv:14©r«  r~   r   ©rH  c                 s   ó    | ]}|V  qd S r’   rs   ©r”   r
  rs   rs   rt   r™   ì  ó   € z.test_minsolve_linear_system.<locals>.<genexpr>)TFc                 s   rN  r’   rs   rO  rs   rs   rt   r™   î  rP  c                      s   t td gˆ dS )Nr}   )rG  r£   rs   ©Ú_qrs   rt   r    ò  s    z-test_minsolve_linear_system.<locals>.<lambda>c                      s   t td gˆ ddS )Nr}   FrF  r£   rs   rQ  rs   rt   r    ó  ó    c                   S   s   t td ddS )Nr}   TrM  r£   rs   rs   rs   rt   r    ö  r™  )rD   rg   rh   ri   r_   rj   r>   r   r¯   rI  r]   r³   )ÚpqtÚpqfrK  r‘  r
  r’  r˜   rs   rQ  rt   Útest_minsolve_linear_systemÍ  sR   

884400ô&ÿ4
þþrV  c                  C   s4   t ddd} tt| d | d  d ƒƒdksJ ‚d S )Nrg   Trö   ry   rz   r}   )r   rá   rD   rç   rs   rs   rt   Útest_real_rootsù  s   (rW  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(	 FrÍ   rŠ   )rg   rh   rá   rD   )r˜   rs   rs   rt   Útest_issue_6528ÿ  s   "&þ rX  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 )Nrg   Trö   rŠ   rÏ   ry   rz   ré   r}   ©rµ  Fr  )r   r   rD   r   r»   )rg   r˜   rs   rs   rt   Útest_overdetermined  s
   (*rZ  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 )
Nrg   rŠ   rx   rz   r   Trö   ry   r‘   )r   rD   r   r   r%   r-   )rg   r`   rs   rs   rt   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)rQ   rg   rs   rs   rs   rt   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   rŠ   ré   r}   Frï  ry   )r-   rl   rk   r   r»   r   rD   rá   ©r‡   rµ   rs   rs   rt   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   )rš   rš   r˜  )rD   r_   r`   ra   rs   rs   rs   rt   Útest_issue_6752(  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‘   rš   r   rz   rŠ   ry   )rD   rg   rY   rs   rs   rs   rt   Útest_issue_6792-  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 yTrö   rz   rx   r}   rF  )r~   rÏ   ré   rn   rš   r   r9  r   rŠ   ry   Únn)ÚnonnegativeÚnz)Únonzeror«   rg   rß   ©Ú	imaginaryr   c                      s   t tˆ ƒd ƒS r~  )rD   rÏ  rs   rç   rs   rt   r    X  r™  zBtest_issues_6819_6820_6821_6248_8692_25777_25779.<locals>.<lambda>r•  rL  r~   r€   )r   rD   rÏ  r   r   r¨   r   r¹   r   r   r   r-   r»   r"   r!   r   r]   r†   r   r%   )rh   rb  rd  r‡   rß   r•  r€   rs   rç   rt   Ú0test_issues_6819_6820_6821_6248_8692_25777_257794  sP   ,(,&&
ÿ.(
ÿ0ÿ &:&6.,,0rh  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   rŠ   )rD   r$   rg   r   r%   rs   rs   rs   rt   Útest_issue_17638p  s   TXXri  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§  re  r{   r   )r   ÚtogetherrB   r©   r@   rž  rD   rá   )rÖ   Útau_cÚtau_1Útau_2ÚphiÚKÚtargetÚK_CÚtau_IÚtau_DÚPIDr‡   ra   ÚvarsÚknownsolutionÚvarrs   rs   rt   Útest_issue_14607x  s,   ÿ6ÿ

þ"ÿrx  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   ©rg   rh   r}   rx   rz   c                      s   t ˆ tˆ ƒtˆˆ  ƒ  ˆ ƒS r’   )rD   r5   r%   rs   ry  rs   rt   r    ¡  r{  z+test_lambert_multivariate.<locals>.<lambda>r   )r„  rg   rh   rJ   r@   r$   rL   rD   rÒ   r%   r#   r   r¨  r-   r]   r†   r¨   )r‡   r—   rs   ry  rt   Útest_lambert_multivariate•  s"   2D20ÿ*6ÿ $" .2rz  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 r~  )rD   r5   rg   r¨   r_   r#   r%   rs   rs   rs   rt   Útest_other_lambert¨  s   ( ÿr{  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}   rš   rŠ   rz   r   r~   ry   éûÿÿÿr   i ØÿÿrÏ   iëÿÿÿr‘   rf   Tr¦  rp  r{   )rD   rg   r$   r   r-   r#   r_   r   r%   rá   r…  r,   rÒ   r   r`   r   rK   rJ   r@   r¨   r3   r/   ri   rh   r   )
r—   Úaxr  r  r\  r]  r^  r_  rf   r‡   rs   rs   rt   Útest_lambert_bivariate¯  sÊ   "  
þ&  
þ28ÿþÿ
ÿ@>"2
ÿ$(
ÿ$ÿ"ý ý $ÿ&ÿ4,ÿ"ý 02ÿ
ÿ"(
ÿ8ÿ"ÿ"ÿ"úr~  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~   rš   r}   rz   )rD   r5   rg   r6   r   r4   r1   r   r-   r   r   r»   r(   r)   r3   rs   rs   rs   rt   Útest_rewrite_trig  s    *@Dÿÿÿÿ
ý$.r  c                  C   sø   ddl m}  tttƒ| tƒ ƒdttddƒtdƒd  tdtdƒ d ƒd  ƒ dttddƒtdƒd  tdtdƒ d ƒd  ƒ dttdƒ d tj	 tddtdƒ  ƒd  ƒ dttddtdƒ  ƒ d tdƒd  tj	 ƒ gkszJ ‚d S )Nr   ©Úsechrx   rš   ry   r~   )
Ú%sympy.functions.elementary.hyperbolicr  rD   r(   rg   r&   r   r-   r   r»   r€  rs   rs   rt   Útest_rewrite_trigh  s   4422ürƒ  c                  C   s  t ttƒ tttdtd td     ƒ } t| tddttttt ƒ  ƒ ttttt ƒ  ƒgks4J ‚tttd ƒtddt  ƒ d ƒdtdtdƒ ƒttddƒƒ d  tdƒd  tdtdƒ ƒ ttddƒƒ d d tdƒd  gdtd	tdƒ d
 d  ƒd  tdƒd  dtd	tdƒ d
 d  ƒd  tdƒd  gfv s©J ‚tttdt ƒd ƒtttƒ d ƒ tdƒ ƒg ksÆJ ‚d S )Nrš   rx   T)Úforcerz   r}   r   iôÿÿÿiÜÿÿÿr‘   )	ri   r%   rg   rh   rD   r-   r$   r   r)   rv  rs   rs   rt   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 r  )rD   r2   rg   r   r-   rs   rs   rs   rt   Ú
test_atan2/  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’   )rD   r7   rg   rh   r:   r8   r9   rs   rs   rs   rt   Útest_errorinverses3  ó      $r‡  c               	   C   sR  t dƒ} tdƒ|  td| d  ƒ | d tdƒtd| d  ƒ d   }t|| ddd }|tddƒtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ   ddtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ     ftddƒddtd	d
ƒtdƒt d  tddƒ    td	d
ƒtdƒt d  tddƒ  fhks§J ‚d S )Nrm   rx   r}   Tr§   ry   rz   rš   éû   rÇ   éo   rF  r  )r   r-   rD   r   r   )rm   r‡   rµ   rs   rs   rt   Útest_issue_2725:  s,   @*ÿÿ$ÿÿÿÿÿ"ÿþr‹  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}   FrÎ  c                 s   s    | ]}|  ¡ V  qd S r’   )Ú	count_ops)r”   rÖ   rs   rs   rt   r™   R  s   € z'test_issue_5114_6611.<locals>.<genexpr>iÆ  )r   r>   rD   r±   rû   rI  )r`   ra   rb   rc   r€   r   re   rß   r  rd   r  rl   rq   rø   rf   rk   r×   r˜   r
  r—   rs   rs   rt   Útest_issue_5114_6611D  s   *@\Lý"r  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}   r˜  rF  rx   )r}   rx   r}   rŠ   )	r>   r   ÚdetrR   r±   rý   r?   rS   rT   )rl   rÖ   rs   rs   rt   Útest_det_quickU  s   ,r  c                  C   s’   t ddd\} }tt| d |d  ƒd | ƒt|d  d ƒ t|d  d ƒgks,J ‚t ddd\} }tt| d |d  ƒd | ƒg ksGJ ‚d S )Nza bTrö   rx   rz   rF  rf  r;  ro  rs   rs   rt   Útest_real_imag_splittinga  s   $ÿ*r  c                  C   sB   dt d  dt d   dt   d } tdd„ t| ƒD ƒƒsJ ‚d S )Nr~   rz   rŠ   rx   ry   c                 s   s    | ]
}t t |¡ƒV  qd S r’   )r   r   r÷   rÞ   rs   rs   rt   r™   k  rñ  z"test_issue_7110.<locals>.<genexpr>)rg   rõ  rD   rÛ   rs   rs   rt   Útest_issue_7110i  s   $r‘  c                   C   s*   t dt ddt   ƒdt gksJ ‚d S rx  )rD   rg   rW   rs   rs   rs   rt   Ú
test_unitsn  rÕ  r’  c                  C   s¢   t dƒ\} }}td|d  | |d  |  | dƒ}t|d|d  ƒ}t| d| |d  ƒ}ttt|||ƒ| ||gdƒƒ}t|ƒttd	gd
gdggƒƒk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>   rC   r   r†  )r‘  r’  rÇ  Úeq1Úeq2Úeq3rµ   rs   rs   rt   Útest_issue_7547r  s   &
þÿr–  c                  C   s*   t ddd} tt| ƒd ƒdgksJ ‚d S )Nr×   Trö   rx   rŠ   r;  )r×   rs   rs   rt   Útest_issue_7895~  r7  r—  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 )Nra  Trö   rx   rŽ   rz   é¿   rÎ   i‡  r‘   FrÍ   )r   r-   r   rD   )rg   rh   r,  r-  r_   r`   r—   rs   rs   rt   Útest_issue_2777ƒ  s   8""r™  c                  C   s"   d} t t|  tƒd | ksJ ‚d S )Ng{[Rs±Ò8r   r£   )Únumberrs   rs   rt   Útest_issue_7322‘  s   r›  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)rš   r}   Úbisect)Úmethod©rC   rg   rs   rs   rs   rt   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  )rC   rg   rh   ri   rs   rs   rs   rt   r    ˜  s   ( c                   S   s   t tt tt fdƒS )Nr–  )rC   rg   rh   rs   rs   rs   rt   r    ™  r£  c                   S   s   t tdk tdƒS )Nr  r}   rž  rs   rs   rs   rt   r    š  r™  )r]   r³   r…   rs   rs   rs   rt   Útest_nsolve–  s   rŸ  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}   rŠ   ry   c                   S   s   t ttd  t d tddS )Nry   r}   F)Ú
incomplete)rD   r_   rg   rs   rs   rs   rt   r    ¢  rv   z.test_high_order_multivariate.<locals>.<lambda>c                    s   g | ]	}t ˆ d  |ƒ‘qS rZ  rX   rÞ   ©rb   rs   rt   r  ¨  r¡   z0test_high_order_multivariate.<locals>.<listcomp>rx   )	rá   rD   r_   rg   r]   r†   rý   r   r»   rs   rs   r¡  rt   Útest_high_order_multivariate  s   &&".$r¢  c                   C   sX   t dt d ƒdgksJ ‚t dtd  d ƒdgksJ ‚t tdddƒddgks*J ‚d S )Nr   r}   rx   zx*(1/x**0 - x)F©Úevaluate)rD   rg   r   rs   rs   rs   rt   Útest_base_0_exp_0­  s
   ÿr¥  c                   C   sd   t dtd  tgƒtƒ ksJ ‚t dtt  tgƒtt hks J ‚t dttdƒ tgƒthks0J ‚d S )Nr}   r   rz   )rU   rg   r¨   rh   r,   rs   rs   rs   rt   Útest__simple_dens´  s   "$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}   rè  ré  rx   rê  rß  rë  Frì  )rá   rD   r-   rh   rg   r   rs   rs   rs   rt   Útest_issue_8755º  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~   ræ  rM  éÍ   éh   rx   TrY  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)rp   rÞ   rs   rs   rt   r™   Ý  rà   z7test_issue_8828.<locals>.<listcomp>.<setcomp>.<genexpr>r	  )r”   r  rs   rs   rt   Ú	<setcomp>Ý  r{  z-test_issue_8828.<locals>.<listcomp>.<setcomp>rs   )r”   rm   rs   rs   rt   r  Ý  r¡   z#test_issue_8828.<locals>.<listcomp>)rg   rh   ri   r-   rD   )r  Úy1Úr1r\  Úy2r]  Úy3Úr3r
  Úf1Úf2Úf3r  Úg1Úg2Úg3r#  r‘  r’  r“  rf   rk   r×   rs   rs   rt   Útest_issue_8828Ã  s,   
$ $
$$


 r·  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~   rF  rx   i,  rƒ  iÂ  )rD   r5   rg   r   rs   rs   rs   rt   Útest_issue_2840_8155á  s   :4<r¸  c                   C   s"   t ddtd   ƒdgksJ ‚d S r×  r£   rs   rs   rs   rt   Útest_issue_9567é  s   "r¹  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   rŠ   rp  r~   )rD   rg   r   r   r-   r+   rh   rá   r+  rs   rs   rt   Útest_issue_11538í  s   .22
ý*
ÿ rº  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   rš   r;  )r_   r`   ra   rb   rc   r€   r   Útermsrµ   rÖ   Ús2Ús3Ús4Ús5rs   rs   rt   Útest_issue_12114ý  s4   66ÿ &(ÿ((ÿ&(ÿ((ÿ÷rÀ  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$J ‚d S r|  )rD   r   rg   rs   rs   rs   rt   Útest_inf	  s   rÁ  c                     sò   t dƒ‰‡fdd„tdƒD ƒ} tdƒ}tt| |ƒƒ}|d d… |dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}| d d… | dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}|| d	   |¡ ¡ ||d	   ¡ kswJ ‚d S )
Nr€   c                    s   g | ]}ˆ |ƒ‘qS rs   rs   rÞ   ry  rs   rt   r  	  rS  z$test_issue_12448.<locals>.<listcomp>rn   zx:15rz   c                    óT   g | ]&}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS ©rŠ   r}   rx   rz   rs   rÞ   ©ra   rg   rh   ri   rs   rt   r  "	  ó    Lÿc                    rÂ  rÃ  rs   rÞ   rÄ  rs   rt   r  &	  rÅ  r   )r   rý   r   r|   rÜ  rD   ÚxreplacerŒ  )Úfunr¼  rÝ  ÚssymÚsfunrs   )ra   r€   rg   rh   ri   rt   Útest_issue_12448	  s&    ÿÿ ÿÿÿrÊ  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}   )rV   rg   rh   ri   rs   rs   rs   rt   Útest_denoms-	  s     ".,2rÌ  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~   rš   r   ry   )r   r   r   r»   r-   rD   )r  r  r\  r]  r^  r_  rŒ  Úsolsrs   rs   rt   Útest_issue_124766	  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rÎ  c                  C   s:   t dƒ} t| tdƒtdƒ  tdƒ | f| ƒg ksJ ‚d S )Nrj   ry   rx   r;  )rj   rs   rs   rt   Útest_issue_13849M	  s   2rÏ  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kiloré   iÀàÿÿ)Úsympy.physics.unitsrÑ  rÒ  rD   rg   rh   rÐ  rs   rs   rt   Útest_issue_14860R	  s   0rÔ  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:4rš   r}   rx   r   r~   rF  r;  )rd   re   r_   r`   rs   rs   rt   Útest_issue_14721W	  s*   ..ýý þý0ÿÿ"ÿÿ0rÕ  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 )
Nrg   Trö   rŠ   é‚   rx   iA  i  r  )r   rD   r-   r   rç   rs   rs   rt   Útest_issue_14779e	  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   Fr£  r   rŠ   rš   iá0  iÕW i¢éÿÿr~   ré   r  rª   rJ  )rD   rh   r
   rg   r   r   )r“  r”  rs   rs   rt   Útest_issue_15307k	  s    ÿ
ÿ 
ÿ" rØ  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}   )rD   rg   r   rh   rs   rs   rs   rt   Útest_issue_15415w	  s
   02>rÙ  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   rÏ   r  r'  r   r}   )rx   rz   rŠ   ry   r‘   rÏ   rŠ   r~   r‘   rz   r5  ré   rF  ry   r`   rš   Tr¦  )rD   r   rg   r-   r   r»   r   r%   r   r   r   )r`   rs   rs   rt   Útest_issue_15731	  s4   >",F," (,D*Fÿ($D"""&rÚ  c                   C   sJ   t td ttd   tƒsJ ‚t ttd  td  td  d ƒs#J ‚d S )NrŠ   r%  rz   rx   r/  )rD   rg   rh   r   rs   rs   rs   rt   Útest_issue_10933Ÿ	  s   ,rÛ  c                  C   s,   t ddd} tt| t ƒ| ƒdgksJ ‚d S )Nrg   Trö   r   )r   rD   rÏ  rh   rç   rs   rs   rt   Útest_Abs_handling¤	  s    rÜ  c                  C   s†   t dƒ} td| d  d|   d dk| dkg| ƒtju sJ ‚t| d d| d   d	|  d  d
 dk| d dkg| gƒtju sAJ ‚d S )Nrg   rx   ry   rÎ   r   g      ø?rz   g)\Âõ( @g=
×£p=L@éj   r}   )r   rD   r   Úfalserç   rs   rs   rt   Útest_issue_7982©	  s   4Jrß  c                  C   sP   t dƒ\} }t| | |  | | | |  | g| |gƒ||d  |fgks&J ‚d S )Nra  r}   r  ry  rs   rs   rt   Útest_issue_14645±	  s   Drà  c                  C   sR   t dƒ\} }ttd| dk f| | dkfƒ| ƒ|td| dk f| dfƒigks'J ‚d S )Nra  r­   r%  T)r   rD   r.   ry  rs   rs   rt   Útest_issue_12024¶	  s    ÿrá  c                   C   s¬   t dt t t tƒtttƒtt  ƒ ttdƒƒ tttƒtt  ƒttdƒƒ gks.J ‚t ttd  td  tƒttdtdƒ dttƒ  dt t  ƒƒgksTJ ‚d S )NrÏ   r  iõÿÿÿ)rD   rg   r   r-   r%   r   r$   r#   rs   rs   rs   rt   Útest_issue_17452¼	  s   4
ÿPrâ  c                   C   s0   t tttdƒd  ƒt  t tƒg ksJ ‚d S rÔ  )rD   r7   rg   r   r   r   rs   rs   rs   rt   Útest_issue_17799Â	  rì   rã  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 )Nrg   Trö   rx   r}   rš   )r   rD   rÏ  r-   rç   rs   rs   rt   Útest_issue_17650Æ	  s   Brä  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   rF  r}   rŠ   rz   )rg   r   rN   rv  rs   rs   rt   Útest_issue_17882Ë	  s   Hræ  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 rz  )rD   r$   rg   rs   rs   rs   rt   Útest_issue_17949Ð	  rˆ  rç  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~   )rp  r   r}   r   r}   )r~   rš   rz   )rD   r   r   rg   Úpowr_   rh   r5   rs   rs   rs   rt   Útest_issue_10993×	  s    * &J,ré  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}   rš   rx   r~   )rg   rh   r   rD   r   )r“  r”  r•  rs   rs   rt   Útest_issue_11553à	  s
   &,rê  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   rŠ   rx   r~   )	r   rD   r3   rg   r5   r1   r-   r   r»   )rj   re   rs   rs   rt   Útest_issue_19113_19102è	  s   "* 
þ4244
ü*rë  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   rŠ   ry   ré   r}   rx   )r   r-   rD   rg   ©r_   r`   ra   rb   rs   rs   rt   Útest_issue_19509÷	  s   ürí  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%   rD   )ÚTHTÚHTÚDBHÚdibÚc0Úc1Úc2Úc3Úc4r€   Úrhsr‡   Útermrµ   rs   rs   rt   Útest_issue_20747
  s   (*ÿ"rù  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   rš   rp  r~   rŠ   r|  )rj   rD   rÒ   rg   r   r   ry  rs   rs   rt   Útest_issue_20902
  s
   FJFJrú  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 )Nr_   Trö   rŠ   ry   )
r   rg   r'   r3   rh   r(   ri   r)   rD   r$   )r_   r¡  Ú	newsystemrs   rs   rt   Útest_issue_21034
  s
   *:6rü  c                  C   sÔ   t ttd t d  td td   td  ƒ t d td   } tt t d td   }t||   t t   ||  ft||   t t   ||  fg}ttd td  td  t t tt  t gttƒ|kshJ ‚d S rz  )r_   r-   rm   r`   ra   rD   rg   rh   )ri   rj   rµ   rs   rs   rt   Útest_issue_4886 
  s   @<@rý  c                  C   sT   t ddd\} }}}t| |t  ||t   tƒt||  ƒt|| ƒ gks(J ‚d S )Nr  Tr¦  )r   rD   rg   r%   rì  rs   rs   rt   Útest_issue_6819'
  s   @rþ  c                  C   s0   t dƒ} td|  t d | ƒdt gksJ ‚d S )Nrg   r}   rŠ   )r   rD   r   rç   rs   rs   rt   Útest_issue_17454,
  s   (rÿ  c                  C   sB   ddt dƒ d  g} tdt t dtd  ƒ d ƒ| ksJ ‚d S )Nr:  rx   )r-   rD   rg   )rÃ   rs   rs   rt   Útest_issue_218521
  s   ,r   c                  C   sŒ   t  ttdt   tdt  dt   ddt    } t| tddd}|ttdt   tdt   t dt   t ddt   gksDJ ‚d S )Nr}   Frï  )rb   r_   ra   rc   r`   rD   r]  rs   rs   rt   Útest_issue_219426
  s   6
ÿÿ
ÿr  c                  C   sP   t td td  t d dd} t td td  t d dd}| |ks&J ‚d S )Nry   rx   r}   F)ÚcubicsTr£   )r,   Úradrs   rs   rt   Útest_solver_flags=
  s     r  c                  C   s’   dt d  dtd d  td   } t|  ¡ t dddt td d  tdtdƒt   td d  t dtdƒt   td d  gksGJ ‚d S )	Nrx   rz   r«   r}   r‘   FrÎ  rš   )rg   rh   ri   rD   r…  r-   r   rv  rs   rs   rt   Útest_issue_22768C
  s   $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~   rš   r}   )rD   rh   r%   rg   r   rs   rs   rs   rt   Útest_issue_22717J
  s   8ÿr  c                     s6   t d d d ‰ tˆ ƒ} t‡ fdd„| D ƒƒrJ ‚d S )Nry   rå  rz   c                 3   s    | ]	}ˆ   t|¡V  qd S r’   )rÒ   rg   rÞ   rv  rs   rt   r™   R
  s   € z#test_issue_25176.<locals>.<genexpr>)rg   rD   rõ  râ   rs   rv  rt   Útest_issue_25176O
  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 )Nrå  ry   rŠ   rx   rz   rp  ré   r|  i  iØÿÿÿé   r}   iìÿÿÿrŽ   i  iöÿÿÿrÎ   )r   r_   rg   r`   ra   rc   r   rb   rd   r-   rI   rv  rs   rs   rt   Útest_issue_10169U
  sV   Fÿÿÿÿ&ÿÿ
ÿÿÿÿÿF
ÿÿý ÿüû

6<6<úr	  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)Útrigrx   rš   )r   r   r5   rj   r3   Úlhsr÷  r…  rI   r1   r-   )r‘  r’  r×   rn  rc   r‡   r‹  rs   rs   rt   Ú*test_solve_undetermined_coeffs_issue_23927f
  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   rP  )rD   r	   rg   rs   rs   rs   rt   r    v
  rS  z"test_issue_24368.<locals>.<lambda>r¼  Trª  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 rË  )rD   r	   rs   ©r€   r¼  rs   rt   r    y
  s   n )r]   r†   r   r*   r   rs   rs   r  rt   Útest_issue_24368s
  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 )NrŽ   rz   r   rÎ   r‘   rx   é°   rŠ   rÃ  rO  r«   r=  éÄ   rQ  r  é   r.  r  ræ  r6  T)r   rD   r.   ÚNaNrg   rs   rs   rs   rt   Útest_solve_Piecewise|
  s(   F*>">"6>"66.
îr  N)rn   (&  Úsympy.assumptions.askr   r   Úsympy.core.addr   Úsympy.core.containersr   Úsympy.core.functionr   r   r   Úsympy.core.modr	   Úsympy.core.mulr
   Ú
sympy.corer   r   Úsympy.core.numbersr   r   r   r   r   r   Úsympy.core.relationalr   r   r   r   Úsympy.core.singletonr   Úsympy.core.symbolr   r   r   r   Úsympy.core.sympifyr   Ú(sympy.functions.combinatorial.factorialsr   Ú$sympy.functions.elementary.complexesr   r   r    r!   r"   Ú&sympy.functions.elementary.exponentialr#   r$   r%   r‚  r&   r'   r(   r)   Ú#sympy.functions.elementary.integersr*   Ú(sympy.functions.elementary.miscellaneousr+   r,   r-   Ú$sympy.functions.elementary.piecewiser.   Ú(sympy.functions.elementary.trigonometricr/   r0   r1   r2   r3   r4   r5   r6   Ú'sympy.functions.special.error_functionsr7   r8   r9   r:   Úsympy.integrals.integralsr;   Úsympy.logic.boolalgr<   r=   Úsympy.matrices.denser>   Úsympy.matricesr?   Úsympy.polys.polytoolsr@   Úsympy.printing.strrA   Úsympy.simplify.radsimprB   Úsympy.solvers.solversrC   rD   rE   rF   Úsympy.solversrG   rH   rI   Úsympy.solvers.bivariaterJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rÓ  rW   Úsympy.polys.rootoftoolsrY   Úsympy.testing.pytestrZ   r[   r\   r]   Úsympy.core.randomr^   rÓ   r„  r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   ru   r„   r‰   r‹   rŒ   r   r   r·   rÄ   rÅ   rÈ   rÉ   rÊ   rÙ   rÚ   rÜ   rã   rä   rå   ræ   rè   rê   rë   rî   rï   rñ   ró   rõ   r  rm  rn  rŠ  rŽ  r  r”  rš  r   r¢  r¥  r©  r¬  r­  r°  r±  r½  rÁ  rÂ  rÍ  rÑ  rÒ  rÓ  r÷  rø  rù  rþ  rÿ  r   r  r  r  r!  r$  r*  r5  r6  r8  r9  rA  rE  rV  rW  rX  rZ  r[  r\  r^  r_  r`  rh  ri  rx  rz  r{  r~  r  rƒ  r…  r†  r‡  r‹  r  r  r  r‘  r’  r–  r—  r™  r›  rŸ  r¢  r¥  r¦  r§  r·  r¸  r¹  rº  rÀ  rÁ  rÊ  rÌ  rÎ  rÏ  rÔ  rÕ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rß  rà  rá  râ  rã  rä  ræ  rç  ré  rê  rë  rí  rù  rú  rü  rý  rþ  rÿ  r   r  r  r  r  r  r	  r  r  r  rs   rs   rs   rt   Ú<module>   sœ    (0D
h$


7
 3('-
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

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