o
    à8Va4p ã                   @   s¨  d dl mZmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZA d dlBmCZC d dlDmEZEmFZFmGZG d dlHmIZImJZJmKZK d dlLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZV d dlWmXZX d dlYmZZZ d dl[m\Z\m]Z]m^Z^m_Z_ d d	l`maZb d d
lcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZr ddd„Zsdd„ Ztdd„ Zudd„ Zvdd„ Zwdd„ Zxdd„ Zydd„ Zzdd„ Z{dd„ Z|d d!„ Z}d"d#„ Z~d$d%„ Zd&d'„ Z€d(d)„ Zd*d+„ Z‚d,d-„ Zƒd.d/„ Z„d0d1„ Z…d2d3„ Z†d4d5„ Z‡d6d7„ Zˆd8d9„ Z‰d:d;„ ZŠe]d<d=„ ƒZ‹d>d?„ ZŒd@dA„ ZdBdC„ ZŽdDdE„ Ze\dFdG„ ƒZdHdI„ Z‘dJdK„ Z’dLdM„ Z“dNdO„ Z”dPdQ„ Z•dRdS„ Z–dTdU„ Z—dVdW„ Z˜dXdY„ Z™dZd[„ Zšd\d]„ Z›d^d_„ Zœd`da„ Ze^dbƒdcdd„ ƒZždedf„ ZŸdgdh„ Z e\didj„ ƒZ¡e\dkdl„ ƒZ¢e]dmdn„ ƒZ£dodp„ Z¤dqdr„ Z¥dsdt„ Z¦e\dudv„ ƒZ§dwdx„ Z¨dydz„ Z©d{d|„ Zªd}d~„ Z«dd€„ Z¬dd‚„ Z­dƒd„„ Z®d…d†„ Z¯d‡dˆ„ Z°d‰dŠ„ Z±d‹dŒ„ Z²ddŽ„ Z³dd„ Z´d‘d’„ Zµd“d”„ Z¶d•d–„ Z·d—d˜„ Z¸d™dš„ Z¹d›dœ„ Zºddž„ Z»dŸd „ Z¼d¡d¢„ Z½d£d¤„ Z¾e]d¥d¦„ ƒZ¿e\d§d¨„ ƒZÀd©dª„ ZÁe]d«d¬„ ƒZÂd­d®„ ZÃd¯d°„ ZÄd±d²„ ZÅd³d´„ ZÆdµd¶„ ZÇd·d¸„ ZÈd¹dº„ ZÉd»d¼„ ZÊd½d¾„ ZËd¿dÀ„ ZÌdÁdÂ„ ZÍdÃdÄ„ ZÎdÅdÆ„ ZÏdÇdÈ„ ZÐe\dÉdÊ„ ƒZÑdËdÌ„ ZÒdÍdÎ„ ZÓdÏdÐ„ ZÔe\dÑdÒ„ ƒZÕe\dÓdÔ„ ƒZÖdÕdÖ„ Z×d×dØ„ ZØe\dÙdÚ„ ƒZÙdÛdÜ„ ZÚdÝdÞ„ ZÛdßdà„ ZÜdádâ„ ZÝdãdä„ ZÞdådæ„ Zßdçdè„ Zàdédê„ Zádëdì„ Zâdídî„ Zãe\dïdð„ ƒZädñdò„ Zådódô„ Zædõdö„ Zçd÷dø„ Zèdùdú„ Zédûdü„ Zêdýdþ„ Zëdÿd „ Zìdd„ Zídd„ Zîdd„ Zïdd„ Zðd	d
„ Zñdd„ Zòdd„ Zódd„ Zôdd„ Zõdd„ Zödd„ Z÷dd„ Zødd„ ZùdS (  é    )AÚAbsÚAndÚ
DerivativeÚDummyÚEqÚFloatÚFunctionÚGtÚIÚIntegralÚLambertWÚLtÚMatrixÚOrÚPolyÚQÚRationalÚSÚSymbolÚNeÚWildÚacosÚasinÚatanÚatanhÚbinomialÚcosÚcoshÚdiffÚerfÚerfinvÚerfcÚerfcinvÚexpÚimÚlogÚpiÚreÚsecÚsinÚsinhÚsolveÚsolve_linearÚsqrtÚsstrÚsymbolsÚsympifyÚtanÚtanhÚrootÚatan2ÚargÚMulÚSparseMatrixÚaskÚTupleÚnsolveÚooÚEÚcbrtÚdenomÚAddÚ	PiecewiseÚGoldenRatioÚTribonacciConstant)Únfloat)Úsolve_linear_systemÚsolve_linear_system_LUÚsolve_undetermined_coeffs)Ú_filtered_gensÚ_solve_lambertÚ_lambert)
Ú_invertÚunradÚchecksolÚposifyÚ_ispowÚ	det_quickÚdet_permÚ	det_minorÚ_simple_densÚdenoms)Úcm©ÚCRootOf)ÚslowÚXFAILÚSKIPÚraises)Úverify_numerically)ÚaÚbÚcÚdÚeÚkÚhÚpÚxÚyÚzÚtÚqÚmÚRé   c                 K   s   t t| ƒj|fi |¤ŽddS )NT)Z	full_prec)r.   r0   Úevalf)r`   ÚnÚoptions© ro   úB/usr/lib/python3/dist-packages/sympy/solvers/tests/test_solvers.pyÚNS   ó   rq   c                  C   s   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|diksGJ ‚t||d t  t ||gdd|t|d t  igkseJ ‚t| dƒd td gddtd	| dƒdigks~J ‚d S )
NZfgé   é   é   T©Údictr   é   éþÿÿÿ)Úmapr   rd   r+   re   )ÚfÚgZfxZgxro   ro   rp   Útest_swap_back   s    ÿ2<6r}   c              	   C   s*   zt | |ƒ W dS  ttfy   Y dS w )NTF)r+   Ú	TypeErrorÚNotImplementedError)ÚeqÚsymbolro   ro   rp   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   rs   rx   ru   )r‚   r   rd   r\   r-   r   re   r#   ro   ro   ro   rp   Útest_guess_poly0   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 )Nrx   ru   rƒ   )r‚   r-   rd   r   re   ro   ro   ro   rp   Útest_guess_poly_cv@   s   ÿr…   c                   C   s€   t td td d  tƒsJ ‚t ttd  td tdtd  ƒ  tƒs&J ‚t ttƒd ttddƒ ttƒ d  tƒs>J ‚d S )Nrx   rs   ru   )r‚   rd   re   r-   r   ro   ro   ro   rp   Útest_guess_rational_cvK   s
   $ÿ4r†   c                   C   sœ   t ttƒd tƒsJ ‚t dttƒ t tƒsJ ‚t ttƒtt ƒ t tƒs(J ‚t dt d tƒs3J ‚t dt  d tƒs?J ‚t ttt  t tƒsLJ ‚d S )Nrx   rs   ru   é
   )r‚   r#   rd   r   re   r\   r]   ro   ro   ro   rp   Útest_guess_transcendentalV   s   ÿrˆ   c               	      s$  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
 td ft tt ƒt d
tdiks¥J ‚ttd
 thƒd
gks²J ‚ttd
 t thƒtd
igksÂJ ‚tt t d
 t tgƒd
t tfgksÖJ ‚tt t d
 t tgddt d
t igksìJ ‚tt t d
 ƒt d
t igksýJ ‚tttt   d ttgƒtdtdiksJ ‚tt t  td  d ttf} t| Ž tdƒ tdƒftdƒtdƒ fgks;J ‚t| ddiŽttgtdƒ tdƒftdƒtdƒ fhfks[J ‚t| ddiŽttdƒttdƒ ittdƒ ttdƒigks{J ‚tt d  tt   t t t d d	t t  d	 t  }tdd}t|tttgfdtttgi|¤Žtttd d	t   tt dt  tdd	t  igksÊJ ‚| tdd¡ t|tttgfdtttgi|¤Žtd	t t td  d	t  tt dt  tdd	t  i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
   dt d   d	t   d t d t d	   igksEJ ‚tddt  t t
tƒ  ƒg ksXJ ‚ttdd„ ƒ ttt
t ƒt  gƒt tdƒ tdiksuJ ‚tt
t ƒt  t
tƒt fƒt tdƒ ttdƒ iks’J ‚ttt
t ƒt  gt tƒtdƒ dfgk tt d t tƒt d gks·J ‚tg t gƒg ksÂJ ‚tt t d d	 t t d gƒt t d igksÝJ ‚tt t d dt  dt  d	 fƒt t d iksùJ ‚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sJ ‚ttt t ƒtt dƒtt t d ƒgt gddg ks8J ‚ttt t d ƒt dk gt ƒrIJ ‚ttt dƒt d dk gƒtt dƒks^J ‚ttt t ƒtt t d ƒgt ƒg ksrJ ‚tdt ƒg ks|J ‚tt d dgt gddg tƒ fksJ ‚d S )Néýÿÿÿrx   rt   rs   é   rk   c                 3   s$    | ]}t |ˆƒttƒˆ kV  qd S ©N©r+   rd   re   )Ú.0Ú	container©ÚansÚeqsro   rp   Ú	<genexpr>f   s   €" z"test_solve_args.<locals>.<genexpr>rƒ   ru   éÿÿÿÿT©Zimplicité*   ry   rv   r   Úsetrw   ÚexcludeF©Úsimplifyé   é   c                   S   s$   t ttƒttƒ ttƒ ttƒ ƒS r‹   )r+   r#   rd   r)   re   ro   ro   ro   rp   Ú<lambda>”   ó   $ z!test_solve_args.<locals>.<lambda>ç        ©r–   )rd   re   ÚallÚtupleÚlistr–   Ú	frozensetr+   r9   r   r#   r\   r]   r-   r^   rb   rc   ra   rw   ÚupdaterZ   r   r   r&   r   )Úargsr€   Úflagsro   r   rp   Útest_solve_argsb   s~   $
ÿ*,$&* (,","
ÿ*
ÿ*
ÿ8
 2
ÿ :
ÿ2F
ÿ&ÿ,ÿ
ÿ("68*6"*(,r§   c                  C   sÆ  t dt d tƒtddƒgksJ ‚t tdt dƒtƒtddƒgks#J ‚tt td d tƒƒtj tjhks7J ‚tt ttd dƒtƒƒtj tjhksLJ ‚t ttd  tƒtd gks\J ‚ttdƒ} t ttd  tƒ| |  d t	dƒt
 |  d  |  d t	dƒt
 |  d  gks‹J ‚tdƒ\}}}}}}t |t |t  | |t |t  | gttƒt|| ||  || ||   t|| ||  || ||   iksÑJ ‚ttjttji}t tt tt fttƒ|kséJ ‚t tt tt fttfƒ|ksúJ ‚t tt tt fttgƒ|ksJ ‚tt td dt  d tƒƒddtj  tdƒddtj  hks/J ‚tt td d d t tƒƒt	dt	tƒ ƒt	dt	tƒ ƒ t	dt	tƒ ƒt	dt	tƒ ƒ hksaJ ‚d S )Nru   rs   rx   úa11,a12,a21,a22,b1,b2rk   rƒ   ry   )r+   rd   r   r   r–   r   ÚOnere   r3   r-   r
   r/   ÚZeroÚHalfr\   )ZrxÚa11Úa12Úa21Úa22Úb1Úb2Úsolutionro   ro   rp   Útest_solve_polynomial1±   s:   "$(* 
:
ÿ.  þÿ "$ýÿÿr³   c                   C   s   t dtƒg ks	J ‚d S )Nrƒ   ©r+   rd   ro   ro   ro   rp   Útest_solve_polynomial2Õ   ó   rµ   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)
    rx   rs   rƒ   r›   ru   é   r   N)r+   r-   rd   r   ro   ro   ro   rp   Útest_solve_polynomial_cv_1aÙ   s
   ""8r¸   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 )Nrƒ   rx   rs   ru   r·   )r–   r+   rd   r\   r-   r   rª   r3   ro   ro   ro   rp   Útest_solve_polynomial_cv_1bå   s   82r¹   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
    rx   ru   rs   N)r+   rd   r   r«   r
   r-   ro   ro   ro   rp   Útest_solve_polynomial_cv_2ê   s
   **ÿÿrº   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 )Nrt   én   ru   é7   rs   i	  iÓ  F©Úcheckr   rk   r‡   é   é   ©Zexponent)rd   r+   Úsubsrm   ÚtnÚfuncrV   rC   ©r{   ÚsÚrÚresro   ro   rp   Útest_quintics_1ô   s   ,,&	 ÿrÉ   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 )Nrt   rk   rš   Fr½   r   ru   rs   r‡   r¿   rŠ   rx   rƒ   )rd   r+   rÂ   rm   rÃ   rÄ   rV   rÅ   ro   ro   rp   Útest_quintics_2  s    ,*,,,,,ûrÊ   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 )Nrt   ru   rs   rx   )rd   r   r+   ©re   ro   ro   rp   Útest_quintics_3  s   *rÌ   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 )NrŠ   rs   c                 s   s    | ]}t |tƒV  qd S r‹   )Ú
isinstancerV   ©r   Úiro   ro   rp   r’   '  ó   € z&test_highorder_poly.<locals>.<genexpr>)r+   rd   r    Úlen)Úsolro   ro   rp   Útest_highorder_poly$  s   &rÓ   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 functionsru   rs   rx   N)r+   rd   re   r-   ro   ro   ro   rp   Útest_solve_rational*  s   <rÔ   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 )Nrs   Trv   )r+   rd   re   r#   r-   ro   ro   ro   rp   Útest_solve_nonlinear/  s   26ÿrÕ   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 )Nrd   rs   rx   rƒ   )r/   r+   r   ©rd   ro   ro   rp   Útest_issue_86665  s   <(r×   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 )Nrƒ   rs   é   r‰   )r+   rd   r   r   r«   ro   ro   ro   rp   Útest_issue_7228;  s   :rÙ   c                   C   s0   t ttd ƒttd ƒ tƒtdƒgksJ ‚d S )Nru   r‡   )r+   r%   rd   r-   ro   ro   ro   rp   Útest_issue_7190?  ó   0rÚ   c                  C   s<   t dƒ} | t| d d ƒ }| | ¡}t|| ƒg ksJ ‚d S )Nrd   rs   rx   )r/   r-   r   r+   )rd   r{   Zf_diffro   ro   rp   Útest_issue_21004C  s   
rÜ   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, nrx   rs   rt   r‰   rŠ   rk   r   ry   )r“   r   rx   r   r   )r/   r+   r   rD   )rd   re   rf   rg   rm   ÚMro   ro   rp   Útest_linear_systemJ  s   222<"þ*ÿ>rÞ   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      $@g     à…@)rx   rx   rx   g      Y@)r   rß   g      @g      i@)g      Àr   r   r   r   g      NÀg      d@)r   rD   rd   re   rf   )rÝ   ro   ro   rp   Útest_linear_system_xfail^  s   ý&rà   c                  C   sš   t dƒ} t| ddƒ| ddƒ | ddƒ | ddƒ | ddƒ | ddƒ g| ddƒ| ddƒ| ddƒ| ddƒƒ| ddƒ| ddƒ | ddƒ| ddƒ iksKJ ‚d S )Nr\   r   rx   )r   r+   )r\   ro   ro   rp   Útest_linear_system_functioni  s   > ÿ&ÿrá   c                  C   s2   dd„ } t ddƒD ]}| |ƒ\}}t||ƒ q	d S )Nc           
         sÔ   d|  d }t ddd\‰ }}t d | ¡dd}t d | ¡dd}t d |d ¡dd}t‡ fd	d
„t|ƒD ƒƒ}g }t| ƒD ]&}	| | ˆ |	¡ ˆ |i¡||	  ¡ | | ˆ |	¡ ˆ |i¡||	  ¡ q?||fS )Nrs   rx   z	x, x0, x1T©Úrealzy0_:{}zy1_:{}zc_:{}c                    s   g | ]
\}}|ˆ |  ‘qS ro   ro   )r   ÚoZcoeffrÖ   ro   rp   Ú
<listcomp>z  ó    zMtest_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqs.<locals>.<listcomp>)r/   ÚformatÚsumÚ	enumerateÚrangeÚappendr   rÂ   )
ZwyZorderÚx0Úx1Zy0sZy1sr^   Úexprr‘   rÏ   ro   rÖ   rp   Ú_mk_eqsq  s   $&z9test_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqsrx   rØ   )rê   r+   )rï   rm   r‘   r^   ro   ro   rp   Ú(test_linear_system_symbols_doesnt_hang_1o  s
   þrð   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$ƒd “|td%ƒ d “|td&ƒ d “|td'ƒ d( “|td)ƒd( “|td*ƒ d “|td+ƒd, “|td-ƒ d “|td.ƒd  “|td/ƒ d |td0ƒd i¥}t| t |d1 ƒ ƒ}t||ƒ|ksüJ ‚td2ƒ}t||  t |d1 ƒ ƒ}t||ƒ|ksJ ‚d S )3N)éB   é   é'   é2   éX   é(   é%   é`   r›   éA   é   é   r÷   éH   r›   é   r¼   r÷   é   éL   )r‡   é]   é"   éb   é;   é,   éC   éJ   r  é^   éG   é=   é<   é   rŠ   rs   é9   rØ   é   éN   )rý   é[   r  é   é@   rù   rò   é5   éM   r  éU   é:   éW   ró   ró   rÀ   é$   r  r  ru   )r  éF   rk   r  éD   é+   éV   éS   éQ   rü   é   é.   r  é   r  r  r  ró   é?   rŠ   )éE   rö   r  é   r  rö   r   r  r   r  r  éY   é>   rú   é   é&   é   r¿   rš   r  )rô   é   r  rÿ   r  é-   rý   rÿ   rþ   rþ   rû   éc   éa   éR   rØ   r  r+  r  r  é#   )r  r(  r*  rõ   r‡   r  é	   r  éZ   r-  r   é)   r  r  r*  r  r)  rõ   rò   ró   )r•   r#  r  r  rŠ   é!   r  r  r  rk   r  éK   r  r   r  r  r%  rü   r¿   rò   )rÀ   rØ   rs   rü   r  é4   rø   rt   é    é3   rú   r  éO   rõ   r  r  r  é   r2  r  )rý   rú   r&  r  r  ró   r!  rþ   rý   rš   r›   é1   r÷   rñ   r'  r  ru   r  r	  r6  )r  r-  éP   r9  r8  r  rx   r÷   rs   r  é6   r-  r8  é/   r;  r/  r.  r   r+  rö   )rk   r9  r-  r  r   r  r*  r  r*  r,  rk   r  é0   r4  rñ   rò   r%  r;  r,  r÷   )r%  r  éI   r  r4  r  rþ   r'  r   r  é\   r'  r,  r  r  r  r8  r0  r  r*  )rs   r5  r  rò   r  r÷   r  r  rt   r1  r,  rù   r   r  rù   r*  r  rõ   r"  rô   )rö   é8   rx   r  r7  r  r7  r%  r÷   rþ   r*  r<  ru   rx   r5  r  r  r.  éT   r5  )r2  rk   r  r7  rù   r/  é   r!  rò   rý   r  rþ   r  r¿   r  rø   rA  r  r   rx   )r,  r(  rš   r4  rx   rs   rô   rB  r4  rÿ   rý   r-  r1  r>  r6  r7  r  ru   r-  rø   )rö   rþ   r4  r‡   r‡   r  r@  r  r-  rt   r  r=  rx   r8  r›   r(  rô   rÿ   r  r4  )r'  r$  r  r  r  r4  r0  r  r  r   r  r¿   r  rõ   r=  rø   rõ   r  rB  ru   zx:19l	   ³fœX·j"Ìbµ!SBs= l	   Ì0e7HPÈég%Oï0 l   B>é tsypYÎ/l   s LYÀr%ú9És;Ll   eAnA²&d%â$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 ©rx   re   )r   r/   r   r¢   r+   r   )rÝ   Úsymsrì   rí   Úx2Úx3Úx4Úx5Zx6Zx7Zx8Zx9Zx10Zx11Zx12Zx13Zx14Zx15Zx16Zx17Zx18rÒ   r‘   re   ro   ro   rp   Ú(test_linear_system_symbols_doesnt_hang_2Œ  s‚   í2ÿþýüûúùø	÷
öõôóòñðïírI  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 )Nrm   )rx   rs   r   rx   rx   ru   rs   rƒ   r“   r‰   r(  rš   rŠ   )r   r   rE   rd   re   rf   )rm   rÝ   ro   ro   rp   Útest_linear_systemLUÃ  s   *"þrJ  c                     sÈ  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tdƒ tdƒt ttdƒd ƒ  tdddtddƒ  d  ƒ d ƒ  dtdƒ  tdƒdtdtdƒ tdƒt tdtdƒ ƒ  tdddtddƒ  d  ƒ ƒ  dtdƒ  tdƒdtdtdƒ tdƒt tdtdƒ ƒ  tdddtddƒ  d  ƒ ƒ  dtdƒ  tdƒdttdƒ d tdƒt ttdƒd ƒ  tdddtddƒ  d  ƒ ƒ  dtdƒ  tdƒdttdddtddƒ  d  ƒ ƒ  dtdƒ  g}||ks(J ‚tˆ  ¡ tƒ|ks4J ‚ttttƒ t	 tƒt
t	t ƒ dt  t
t	t ƒgksSJ ‚tttdt ƒ t	 tƒt
t	t ƒ d t t
t	t ƒd gksvJ ‚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sÈJ ‚tt	|t | t   tƒ|  t	 t	|  g| t	 |t	  gfv sëJ ‚tt	|t| t ƒ  tƒ| tt	| ƒ gksJ ‚tt	|d| t    tƒ|t	 | t	  gt	| | t	   gfv s'J ‚tt	| t|   tƒt	|  d|  gks>J ‚ttt t	 tƒtt	ƒttƒ gksSJ ‚tdt d tƒdtdƒtdƒ  gksjJ ‚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sJ ‚ttt	 d ƒtdit	digks J ‚ttt	 d gƒtdit	digks´J ‚ttt	 td t	d   ƒtditt	 itt	it	digksÔJ ‚ttt	 td t	d   gƒtditt	 itt	it	digksõJ ‚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s#J ‚tdƒ‰tt	ˆtdƒt ƒ t	ˆtdƒt ƒ  tƒdgksDJ ‚tˆtƒˆdƒ tƒdgksUJ ‚tˆtƒˆdt ƒ tƒdgkshJ ‚tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ ttdd„ ƒ ttdd„ ƒ ttttƒƒƒdtd gks«J ‚tddd d!\} }ttt| d"tt| ƒd  ƒ|ƒƒd#ksËJ ‚tt	dt  t tƒtt	ƒttƒ gksâJ ‚d S )$Nr   ©r\   r]   ru   rs   rƒ   r›   rt   iíÿÿÿrØ   éüÿÿÿc                 3   ó(    | ]}ˆ   t|¡jd ddkV  qdS ©T)Zchopr   N©rÂ   rd   rm   ©r   r\   ©r€   ro   rp   r’   ð  ó   €& z,test_solve_transcendental.<locals>.<genexpr>rx   rŠ   rÀ   r/  ia	  r“   r¿   r‰   r‡   r{   c                      s   t ˆ ttƒˆ ddƒ tƒS ©Nrx   rs   rŒ   ro   ©r{   ro   rp   rœ   %  ó    z+test_solve_transcendental.<locals>.<lambda>c                      s   t ˆ ttƒˆ dt dƒ tƒS ©Nrs   rŒ   ro   rT  ro   rp   rœ   &  ó    c                      s   t ˆ ttƒˆ dt ƒ tƒS ©Nrx   rŒ   ro   rT  ro   rp   rœ   '  ræ   c                      s   t ˆ ttƒˆ dƒ tƒS rX  rŒ   ro   rT  ro   rp   rœ   (  ó    c                   S   s0   t ttƒtttƒƒ ttƒtttƒƒ  d ƒS ©Nru   )r+   r*   rd   r   ro   ro   ro   rp   rœ   .  rÛ   c                   S   s   t td t t d tƒS ©Nrs   ru   rŒ   ro   ro   ro   rp   rœ   2  rU  za, bTF)rã   Únegativeç      à?zP[2.0 - 0.318309886183791*acos(1.0 - 2.0*a), 0.318309886183791*acos(1.0 - 2.0*a)])Ú	sympy.abcr\   r]   r+   r#   rd   r%   r–   r   re   r   r&   r   r)   r-   r   r   r   r
   rÑ   r    Úexpandrf   r   r   rZ   r   Ú
ValueErrorr/   Ústr)r\   r]   r   Úresultro   )r€   r{   rp   Útest_solve_transcendentalÐ  sÖ    80<&þþ""þ
ú"	$"(0 (
ÿ4@
*<"(
&ÿÿÿ
ÿ"ÿÿ
ÿ"ÿÿ
ÿ(ÿÿ
ÿ:ø	>F,&þ.F2F.*."$&(@B*2:"&""
ÿ2rc  c                  C   sz  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¡d
||ƒ |¡d
iksçJ ‚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s;J ‚d S )Nrg   rd   re   r¨   rx   ru   rs   rƒ   r{   r]  r   )r   r   r/   r+   r   r   )rg   rd   re   r¬   r­   r®   r¯   r°   r±   ZsolnÚeqnsr{   ÚFro   ro   rp   Ú$test_solve_for_functions_derivatives@  sn   0  
þ",ÿÿÿ(&
ÿ$.& 4 ÿÿ
ÿ( ÿ@ÿ,6ÿÿÿ2rf  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{   rs   rƒ   rx   )r   rd   r   r+   )r{   re  r`   ro   ro   rp   Útest_issue_3725s  s    
Brg  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 drs   )r   rs   r‰   r   )rx   rs   ru   rƒ   rx   r“   ru   ry   r   )r/   r   r+   r   r   )r\   r]   r^   r_   ÚAÚBÚCro   ro   rp   Útest_issue_3870z  s   8:::>B<BLrl  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   rx   ©r—   ©r/   rs   ru   r   rx   ry   ©r   r   r“   c                   S   s   t ttdƒdƒS rZ  )r,   r   rd   ro   ro   ro   rp   rœ   §  ó    z#test_solve_linear.<locals>.<lambda>)
r   r,   rd   re   r   r)   r   r#   rZ   r`  )rm  r€   ro   ro   rp   Útest_solve_linear  s6   .(.&&""ÿ2*4*&"$rs  c                   C   s$  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 ‚d S )Nrs   rx   ry   r“   )rF   r\   rd   r]   r^   ro   ro   ro   rp   Útest_solve_undetermined_coeffsª  s&   @ÿ6
ÿ(ÿÿ
ÿÿ
ÿþrt  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 )Nrd   rx   rs   r   r“   Trâ   ru   rŠ   rt   F)r   r   r   rª   r;   r+   r   r	   r   r-   r   r)   r«   r&   r   r©   r   )rd   rÒ   Úsystemro   ro   rp   Útest_solve_inequalities¶  sD   $ÿÿÿ$6ÿ428****4rv  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 )Nrx   rt   rs   ru   ry   r   r“   rƒ   rÀ   c                 3   rM  rN  rO  rP  rQ  ro   rp   r’   ê  rR  z"test_issue_4793.<locals>.<genexpr>TrŸ   c                   S   s   t ttƒttƒ tƒS r‹   )r+   r%   rd   r#   ro   ro   ro   rp   rœ   ñ  ó    z!test_issue_4793.<locals>.<lambda>c                   S   s   t dt ttƒ d ƒS r[  )r+   rd   r#   ro   ro   ro   rp   rœ   ò  rY  )r+   rd   r-   r#   re   r%   r)   r   rÑ   r    rf   rZ   r   ©r   ro   rQ  rp   Útest_issue_4793Ý  s,   .. $ B
&&8þB&"ry  c                  C   s8  t ttƒƒt ttd ƒƒ  krdgksJ ‚ J ‚t ttd ƒƒdgks&J ‚tdƒ} t d|  ttƒ tƒg ks9J ‚t dt td  d tƒdgksKJ ‚tt td dt   t¡ƒƒtjtdƒhkscJ ‚td	ƒ}t dd
t |tƒ  |tƒ |tƒƒtt	d
dƒ gks„J ‚t dt
d
t d
ƒ d tƒt	ddƒgksšJ ‚t ttƒtttƒƒ d ƒt	ddƒtdƒd  d gks¸J ‚tt ttttƒƒttt ƒƒ d ƒƒƒttdƒ d d ƒttdƒd d ƒhdttdƒ d ƒ dttdƒd ƒ htdtdƒ d ƒtdtdƒ d ƒhfv sJ ‚tt tttƒtt ƒ d ƒƒƒttdƒ d ƒttdƒd ƒhks2J ‚tt tt tdt   d tƒƒt	ddƒtd
ƒd  dt  t	ddƒtd
ƒd  dt  hksdJ ‚t ttt ƒtt t ƒ d tƒtt tdƒ gks‚J ‚t tt tt  d tƒtdƒttƒttƒ  gtdƒttt ƒ gfv sªJ ‚tj}t tdt ƒtdƒ tƒdt|t	ddƒtdƒt d   ƒt|t	ddƒtdƒt d   ƒgdt| d tdƒ| t d  ƒt| d tdƒ| t d  ƒgfv sJ ‚tddd}t d| d |d  ƒg ksJ ‚d S )Nru   r   rx   r\   r‰   rs   rÀ   rB  r{   rt   r/  i´~ûÿi©æ  rƒ   r“   r   rL  rc   T©Úpositive)r+   r-   rd   r   r–   r   r   rª   r   r   r3   r   r#   r%   re   rf   ÚExp1r
   )r\   r{   r<   rc   ro   ro   rp   Útest_PR1964õ  sF   2$0:,<(((&ý
ÿ  
ÿ :
ÿ<ÿ.
ÿDDþ&r}  c                  C   s  t ddd} t| d d | ƒg ksJ ‚t dddd}t|d |d  d| d  |ƒdgks0J ‚t ddd} t d	ƒ}t| d
|  d d|  d|  d g| |ƒg ksTJ ‚t| | | |d  d | |ƒtdƒtdƒ fgkspJ ‚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sÆJ ‚d S )Nrd   Trâ   rs   rx   rm   )Úintegerr{  rz  re   rt   r‰   rŠ   rk   rv   zx y z)r   r+   r-   r#   r/   )rd   rm   re   rf   ro   ro   rp   Útest_issue_5197"  s   ,48>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 )NFr½   Trx   rs   ru   )r–   r+   rd   re   r-   r   rª   ro   ro   ro   rp   Útest_checking4  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 )Nrs   rx   rt   rk   zC1 C2r{   r\   rƒ   r‰   r“   ru   ry   )r+   r-   rd   r#   re   r%   r
   r&   r/   r   r   r   r|  r)   r   r*   r   r–   r   r1   )ZC1ZC2r{   r\   r<   ro   ro   rp   Útest_issue_4671_4463_4467>  s>   &
ÿ(>
ÿJ$$
þ  
þ$$þ@6(&&ÿ
ÿ$r  c               	   C   sH  t dƒ\} }tt| td  td  t|ƒtt  gttgƒƒt| t|ƒd  ƒ dt| t|ƒd  ƒ t|ƒ ft| t|ƒd  ƒt| t|ƒd  ƒt|ƒ fhksTJ ‚tttƒt	tƒ dt d gttgƒt
t	tddƒƒƒtddƒfgksxJ ‚tttƒt	tƒ dttƒ d gttgƒt
t	t
dƒƒ ƒt
dƒ fgksžJ ‚ttttƒt	tƒ td d gttgƒƒt
t	dƒ ƒtdƒ ft
t	dƒƒtdƒfhksËJ ‚ttƒd t	tƒ td  dttƒ d g}t|ddttgt
dƒ ttdt ƒ t	t
dƒƒ ƒft
dƒ ttdt ƒ t	t
dƒƒ ƒ fhfksJ ‚t|ttddttgtttdt ƒ t	tƒ ƒftttdt ƒ t	tƒ ƒ fhfksEJ ‚tt|ttƒƒt
ttd  t	t
dƒƒ ƒ ƒt
dƒ ft
td  t	t
dƒƒ ƒd t
dƒ fhksyJ ‚tt|ttƒƒt
dƒ ttdt ƒ t	t
dƒƒ ƒ ft
dƒ ttdt ƒ t	t
dƒƒ ƒfhks­J ‚ttƒd t	tƒ t dttƒ d g}t|ddttgt
dƒ tdt ƒ t	t
dƒƒ fhfksáJ ‚t|ttddttgttdt ƒ t	tƒ fhfksþJ ‚tt|ttƒƒt
tt t	t
dƒƒ ƒ ƒt
dƒ ft
t t	t
dƒƒ ƒd t
dƒ fhks.J ‚t|ttƒtdt ƒ t	t
dƒƒ t
dƒ fgksJJ ‚tttd td  ƒtd	ƒ tt d fddttgtjtdƒftdƒtjfhfkswJ ‚ttttd td  ƒtd	ƒ tt d fttƒƒtjtdƒftdƒtjfhks¢J ‚d S )
Nzr,trs   r“   rx   ru   rƒ   TrŸ   r‡   )r/   r–   r+   rd   re   r1   r-   r   r#   r)   r%   r   r   rf   r©   )rÇ   rg   r‘   ro   ro   rp   Útest_issue_5132[  sr   02ÿ.þÿ$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?rs   rx   T)ÚmanualZminimal©r/   re   rd   rÑ   r+   ©ZlamZa0Zconcr\   r]   r‘   Úsymro   ro   rp   Útest_issue_5335‡  s   ."
þ
rŠ  ZHangsc                  C   sœ   t dƒ\} }}d}d}| dt  |dtd   t  |t d t  |dtd   t dt  |t  tt | g}tt|g}tt||ddƒdksLJ ‚d S )Nrƒ  r„  r…  rs   rx   F©Zrationalr‡  rˆ  ro   ro   rp   Ú_test_issue_5335_float”  s   ."
þ
rŒ  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 )Nrs   rƒ   )r–   r+   rd   re   r-   ro   ro   ro   rp   Útest_issue_5767¡  s    ÿr  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 )Nrs   ru   rx   rt   rƒ   )r–   r+   rd   re   r   r©   r-   ro   ro   ro   rp   Útest_polysys¦  s   ,"ÿÿ(,ÿÿ
ÿÿrŽ  c            	   
      sT  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 ‚d S )ˆNc                   S   s,   t ttƒttd ƒ tdttƒ ƒ d ƒS ©Nrx   ru   )rK   r-   rd   ro   ro   ro   rp   rœ   ²  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 )Nrx   ru   rs   )rK   r-   rd   r   re   ro   ro   ro   rp   rœ   ´  ó   *rÆ   )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 ©Nrx   r   )Úboolr_  )Úrvr   r`   r\   )Ús_checkro   rp   r¾   »  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   rx   )r¢   Úatomsr   ÚziprÑ   rÂ   r_  ra  )r”  r   r_   Úreps©rÆ   ro   rp   r•  Ã  s   66&ÿztest_unrad1.<locals>.s_checkrx   ru   rs   rŠ   rt   r  ry   r›   r/  rƒ   r  ix  iè  ià  i  rØ   iÜ  iæ	  i¼  é©   r1  rö   éè   é    Fr½   z32*sqrt(x)*(x + 1)**(1/3) + x - 4*y + (x + 1)**(2/3)r  rÀ   iúÿÿÿr“   r   rš   r9  r‡   r·   r   rû   c                   S   s(   t ttƒttdƒ ttd dƒ d ƒS )Nru   rx   rt   rs   )r+   r-   rd   r3   ro   ro   ro   rp   rœ   +  s   (c                   S   s   t tdƒ ttƒt  ƒS rV  )r+   r-   r   rd   ro   ro   ro   rp   rœ   .  rU  rò   r)  éÔ   éÀ   r@  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 )Nrs   ru   rƒ   rt   rx   )rK   r3   rd   rÂ   ro   ro   ro   rp   rœ   H  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)]ró   r:  r&  r8  T)Z_reverserB  r>  é»   é  éä   r$  r  r5  rk   z!(x+y)**(2*y/3) + (x+y)**(1/3) + 1é þÿÿé@  é˜  é®  ©Z_unradz9-x + (7*y/8 - (27*x/2 + 27*sqrt(x**2)/2)**(1/3)/3)**3 - 1r#  i   iW  i   iÀ  r=  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0.73re  ©r™   r¾   c                 3   s    | ]
}|ˆ    ¡ jV  qd S r‹   )r_  Zis_zerorP  rx  ro   rp   r’   ­  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™   r6  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 )Nru   rt   )rK   r3   rd   re   ro   ro   ro   rp   rœ   Ó  s   & ) rZ   r   r/   r   rK   r-   rd   r3   r   r\   r]   r^   re   r_   r   r©   r–   r+   rª   r   rM   r
   rg   r   r«   rÑ   rq   r   ÚreversedrÂ   r   Úany)	r¾   r€   rf   rc   r`   re  ÚXZxiÚYro   )r   rÆ   r•  rp   Útest_unrad1°  s*  ÿ
ÿ"ÿÿÿ$ÿÿ$ÿ4:
ÿ
ÿ
ÿ$
ÿ&26þ22
ÿ*$
ÿ&*
ÿ(

ÿ&.
ÿ"
ÿ
ÿ"&(8@.*,
ÿ<8<((0 &$ 0.("*ÿ**
ÿ"
ÿ&$ÿ*Nÿÿÿ
ÿ02
ÿ 
ÿ 
ÿ("
ÿ*"
ÿ**
ÿ*Bÿÿÿÿ
ÿ(02
ÿ,.
ÿ(6ÿ
ÿ(Bÿ
ÿBÿ
ÿ,Jÿÿÿ
ÿ&F
ÿþ	&
ÿ6,,ÿÿÿÿ
ÿH
ÿ
ÿÿÿ
ÿÿÿ

ÿ
ÿÿÿÿ
ÿÿÿ"ÿü"2
ÿN
ÿÿÿ
ÿ.2ÿ
ÿ.:
ÿ
ÿ
ÿ
ÿÿÿÿ
ÿ.:
ÿ
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>(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 )Nrx   rƒ   rs   )r-   rd   r+   r   r«   rQ  ro   ro   rp   Útest_unrad_slowá  s   Dr±  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 )
Nru   rs   rx   rt   r“   rƒ   rØ   r‡   r   )r+   r3   rd   r   rV   ro   ro   ro   rp   Útest_unrad_failé  s   6&Bÿr²  c                     sî  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t‡ fdd„ƒ tt‡ fd	d„ƒ d S )
Nz
x, y, r, trs   rx   TFr   c                      s
   t ˆ dƒS rX  ©rL   ro   rÖ   ro   rp   rœ     s   
 ztest_checksol.<locals>.<lambda>c                      s   t g ˆ dƒS rX  r³  ro   rÖ   ro   rp   rœ     s    )	r/   r-   r1   rL   r   r   r   rZ   r`  )re   rÇ   rg   r€   Zdict_var_solnro   rÖ   rp   Útest_checksolò  s$   &ÿ    ($$ r´  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 )Nrs   )rs   r   rx   ru   r   )rJ   rd   r#   r%   r\   ro   ro   ro   rp   Útest__invert  s
   *6rµ  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 )Nrs   ru   rƒ   )r+   r\   rd   r%   r#   r   ro   ro   ro   rp   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:rrx   TF)r†  r¾   r™   )r/   rÑ   r+   )r\   r]   r^   r_   r`   r{   r|   rb   rÏ   Újra   Úlri   rm   rä   rc   rh   rÇ   rD  r‘   ro   ro   rp   Útest_issue_5114_solvers  s   ,****û"r¹  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|¢R ddddœŽˆ ks¹J ‚t|g|¢R dddœŽˆ d ksËJ ‚t|g|¢R ddiŽg ksÚJ ‚t|g|¢R Ž g ksæJ ‚‡ 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,Q4ry   rs   ru   rš   rL  rØ   rƒ   rŠ   rò   TF)r†  r¾   rw   ©r†  r¾   r   r†  c                    s   g | ]	}|  ˆ d  ¡‘qS ©r   )rÂ   )r   Zeirx  ro   rp   rå   J  s
    ÿÿz#test_issue_5849.<locals>.<listcomp>©r/   r+   )ÚI1ÚI2ÚI3ÚI4ÚI5ÚI6ÚdI1ÚdI4ÚdQ2ÚdQ4ÚQ2ÚQ4r`   Úvro   rx  rp   Útest_issue_5849$  s<   


*÷$ù	"$
ÿÿrÌ  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.
    rº  r»  ry   rs   ru   rš   Nr¾  )r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  r`   ro   ro   rp   Útest_issue_5849_matrixN  s   



*÷$rÍ  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sÏJ ‚d S )Nza, b, c, d, f, g, krt   rŠ   rs   r/  rƒ   ru   r  r(  r¿   r   ry   Trv   )r/   r   r+   )
r\   r]   r^   r_   r{   r|   ra   ZunknownsZ	equationsZanswerro   ro   rp   Útest_issue_21882i  s    <" ÷$&ýrÎ  c                     s*  t tdƒ\‰ } }tdƒ}tˆ tƒtƒ}t| |ƒ|ƒ}tˆ tƒˆ tƒ t¡ ˆ tƒƒ| gks0J ‚tˆ tƒd ˆ tƒƒdgks@J ‚tˆ tƒdˆ tƒ t¡  ˆ tƒƒd| gksYJ ‚tˆ tƒdˆ tƒ t¡  gˆ tƒƒˆ tƒd| iksvJ ‚tˆ tƒdˆ tƒ t¡  ˆ tƒd t d gˆ tƒtƒˆ tƒd| td|d  d igks¦J ‚tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒdd| |ƒgt||ƒd ˆ |ƒd  | ƒ ˆ |ƒ ft||ƒd ˆ |ƒd  | ƒˆ |ƒ fhfksJ ‚ˆ tƒ td¡ˆ tƒ| tƒ  | tƒd  d ˆ tƒ| tƒg}t	t|Ž ƒtdƒ tdƒftdƒtdƒ fhks=J ‚ˆ tƒd | tƒ dˆ tƒ t¡  | tƒd d g}t|ˆ tƒ| tƒddˆ tƒ| tƒgtd| d ƒ t
dƒftd| d ƒt
dƒftd| d ƒ t
dƒ ftd| d ƒt
dƒ fhfks¡J ‚tt‡ fd	d
„ƒ tˆ tƒˆ tƒ t¡ tgdˆ tƒtˆ tƒtƒ dfksÊJ ‚tˆ tƒttttfƒ tgdˆ tƒttttfƒ dfksêJ ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ dfksJ ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ fks1J ‚ttˆ tƒ|  ˆ tƒd |  tgdtd| fksOJ ‚tttdt tƒ ƒtdfksaJ ‚tttttƒ tgdtdfkstJ ‚tttttƒ d tgdtdtd  fksJ ‚t	ttttƒd  ttƒƒƒtt ƒ tt ƒhksªJ ‚ttttƒ tddttƒ gks¾J ‚tttƒttƒ tddg ksÐJ ‚ttttƒ tddttƒgksãJ ‚ttd t d tddtd  d gksûJ ‚ttd t d td ddt d gksJ ‚d S )NZfghr\   ru   rs   rƒ   r/  TrŸ   c                      s$   t ˆ tƒˆ tƒ t¡ ˆ tƒgdS )Nrp  )r,   rd   r   ro   rT  ro   rp   rœ   ¦  r   z!test_issue_5901.<locals>.<lambda>rp  rx   ry   r   r”   )rz   r   r   r   rd   r+   r   re   r-   r–   r   rZ   r`  r,   r   r#   r   r)   )r|   rb   r\   ÚDÚGr¥   r‘   ro   rT  rp   Útest_issue_5901‚  s¦   ÿÿ"ÿ$ÿ8 ÿ@ÿ*(þ
þ>
"
ÿ6ü
ÿÿ
ÿ
ÿ"
ÿ"
ÿ(

ÿ
ÿ
ÿ
ÿ
ÿ

ÿ$
ÿ
ÿ
ÿrÑ  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 )Nrs   çš™™™™™¹?Tr‹  r.  r‡   Fc                 s   ó    | ]}|j V  qd S r‹   ©Z	is_NumberrP  ro   ro   rp   r’   É  ó   € z"test_issue_5912.<locals>.<genexpr>c                 s   rÓ  r‹   rÔ  rP  ro   ro   rp   r’   Ë  rÕ  )r–   r+   rd   r   r«   r-   rÑ   r    rx  ro   ro   rp   Útest_issue_5912Å  s   $ÿ"&rÖ  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‹   )rÑ   r–  r   ©Úe1Úe2ro   ro   rp   ÚtestÏ  s   z!test_float_handling.<locals>.testr]  Tr‹  r   Frx   rs   ç      ð?g       @ru   g      @rÁ   rƒ   g!ÌÈ,‹ÿ?éd   gffffffæ?g333333ã?gš™™™™™É?g333333Ó?rÒ  )r+   rd   Zis_RationalZis_Floatr   r«   rC   r¢   r¡   r–   ÚtypeÚitemsr   r#   r   r^   rf   rg   )rÚ  Zcontainr   ra   rË  Ztotro   ro   rp   Útest_float_handlingÎ  s,   ",*(""&"&
ÿ<rß  c                  C   s*   t ddd} t| d d ƒdgksJ ‚d S )Nrd   Trz  rs   rx   r¾  rÖ   ro   ro   rp   Útest_check_assumptionsè  ó   rà  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 )Nru   rx   r‰   rƒ   rs   )r+   r2   rd   r
   r&   r   ro   ro   ro   rp   Útest_issue_6056í  s   (8ÿ"8ÿrâ  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 )Nrs   TF)Z	numerical)rd   r#   r   r%   rL   rQ  ro   ro   rp   Útest_issue_5673õ  s   &rã  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RfTrz  ry   rx   r“   ro  rs   ru   r   rt   rŠ   ©r/   r+   r-   )
rj   rk  ZRiZVoutZV1ZVminusZVplusrÆ   rä  r‘   ro   ro   rp   Útest_excludeû  sL   ÿ"(ý$(üü
ú,@ü,@üû$ üöræ  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 )Nrt   rƒ   ru   rs   rÀ   ZZZ)Údomain)rd   r   r–   r+   r   Z	all_rootsr™  ro   ro   rp   Útest_high_order_roots#  s   *,rè  c                  C   sÌ   dd„ } | t tt t tt t t gdddƒdksJ ‚| t tt t tt t t gdddƒdks6J ‚| t tt t tt t gdddƒdksMJ ‚| t tt t tt t gdddƒdksdJ ‚d S )	Nc                 S   s   t dd„ |  ¡ D ƒƒS )Nc                 S   s   g | ]}|d kr|‘qS r½  ro   )r   rd   ro   ro   rp   rå   *  rY  z>test_minsolve_linear_system.<locals>.count.<locals>.<listcomp>)rÑ   Úvalues)Zdicro   ro   rp   Úcount)  r¶   z*test_minsolve_linear_system.<locals>.countT)Z
particularZquickru   Frx   rs   )r+   rd   re   rf   r\   rg   )rê  ro   ro   rp   Útest_minsolve_linear_system(  s   (ÿ(ÿ.2rë  c                  C   s4   t ddd} tt| d | d  d ƒƒdksJ ‚d S )Nrd   Trâ   rt   ru   rx   )r   rÑ   r+   rÖ   ro   ro   rp   Útest_real_roots3  s   (rì  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†rs   iQÖAiTâkl   1ö'	 iýûa5iPQRiçäžl    d(	 Fr½   rƒ   )rd   re   rÑ   r+   )r‘   ro   ro   rp   Útest_issue_65289  s   "&þ rí  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 )Nrd   Trâ   rƒ   rÀ   rt   ru   rØ   rx   ©r†  Fr¼  )r/   r   r+   r   r«   )rd   r‘   ro   ro   rp   Útest_overdeterminedB  s
   (*rï  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 )
Nrd   rƒ   rs   ru   r   Trâ   rt   rŠ   )r/   r+   r
   r&   r%   r-   )rd   r]   ro   ro   rp   Útest_issue_6605J  s   8& .rð  c                   C   s,   t td ƒsJ ‚t tƒrJ ‚t dƒrJ ‚d S )Nrs   T)rN   rd   ro   ro   ro   rp   Útest__ispowT  s   rñ  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 )Nrs   rƒ   rØ   rx   Fr¨  rt   )r-   ri   rh   r   r«   r   r+   rÑ   ©r€   rÒ   ro   ro   rp   Útest_issue_6644Z  s*   8"ÿÿÿÿ"ÿÿÿÿÿró  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 )Nrs   )r“   r“   rq  )r+   r\   r]   r^   ro   ro   ro   rp   Útest_issue_6752b  s   *:rô  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 )	Nrx   rs   rŠ   r“   r   ru   rƒ   rt   )r+   rd   rV   ro   ro   ro   rp   Útest_issue_6792g  s
   *.((ýrõ  c                     sˆ  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 dƒ‰ ttˆ ƒd tˆ ƒd gˆ ƒtˆ ƒdˆ ddt  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sËJ ‚t ddd}tt|ƒd ƒdt dt gksãJ ‚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s8J ‚t ddd\‰ } tˆ | t  d dt  ƒˆ dt | dt iks[J ‚t ddd‰ tˆ |  d dt  ƒˆ d| dt iksxJ ‚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sÂJ ‚d S )Núx yTrâ   ru   rs   rx   r/  )ry   rÀ   rØ   rk   r“   r	  r"  rd   rÏ   ©Z	imaginaryr‰   c                      s   t tˆ ƒd ƒS rZ  )r+   Úabsro   rÖ   ro   rp   rœ   †  rr  z6test_issues_6819_6820_6821_6248_8692.<locals>.<lambda>rm  )r~  rƒ   r   ry   r{   )r/   r+   rø  r5   r&   r–   r   r©   r   r   r   r-   r«   r'   r$   r
   rZ   r   r   r%   )re   r€   rÏ   rm  r{   ro   rÖ   rp   Ú$test_issues_6819_6820_6821_6248_8692n  s>   ,(,&&
ÿ.
ÿ $:&6.,,0rù  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, Krs   rx   zK_C, tau_I, tau_DT)r{  Znonzerorv   r   )r/   Ztogetherr>   r™   r   Zcoeffsr+   rÑ   )rÆ   Ztau_cZtau_1Ztau_2ZphiÚKÚtargetZK_CZtau_IZtau_DZPIDr€   r^   ÚvarsZknownsolutionÚvarro   ro   rp   Útest_issue_14607Ÿ  s,   ÿ6ÿ

þ"ÿrþ  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   ©rd   re   rx   rs   ru   c                      s   t ˆ tˆ ƒtˆˆ  ƒ  ˆ ƒS r‹   )r+   r)   r%   ro   rÿ  ro   rp   rœ   È  rW  z+test_lambert_multivariate.<locals>.<lambda>r‰   )r^  rd   re   rG   r   r#   rI   r+   rÂ   r%   r   r   r|  r-   rZ   r   r–   )r€   r   ro   rÿ  rp   Útest_lambert_multivariate¼  s"   2D20ÿ*6ÿ $" .2r   c                   C   sn   t dttƒ ttdƒ  tƒdgksJ ‚tt tt tt  ƒtƒtt tttƒ t ƒ ttƒ hks5J ‚d S rZ  )r+   r)   rd   r–   r\   r   r%   ro   ro   ro   rp   Útest_other_lambertÏ  s   ( ÿr  c            
   	   C   s  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sJ ‚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sÅJ ‚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síJ ‚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sgJ ‚t dt ttd ƒ  td¡tƒdttddƒƒ dttddƒtdƒt d  ƒ dttddƒtdƒt d  ƒ dttddƒdƒ gks®J ‚t td td ttƒ  ttddtdtt d ƒ itdttd ƒ igksØJ ‚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 ‚d S )Nrs   rx   r“   rƒ   ru   r‰   ry   rt   éûÿÿÿr   i ØÿÿrÀ   iëÿÿÿrŠ   rc   Trz  rL  rv   )r+   rd   r#   r   r-   r   r\   r   r%   rÑ   r_  r3   rÂ   r
   r]   r/   rH   rG   r   r–   r   r   rf   re   r&   )
r   Zaxrì   rí   rE  rF  rG  rH  rc   r€   ro   ro   rp   Útest_lambert_bivariateÖ  s®   "  
þ&  
þ28ÿþÿ
ÿ@>"2
ÿ$(
ÿ$ÿ"ý ý $ÿ&ÿ4,ÿ"ý 02ÿ
ÿ"(
ÿ8ÿr  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   rs   ry   r“   rx   ru   )r+   r)   rd   r1   r&   r(   r   r   r-   r
   r   r«   r*   r2   r   ro   ro   ro   rp   Útest_rewrite_trig%  s    *@Dÿÿÿÿ
ý$.r  c                  C   sø   ddl m}  tttƒ| tƒ ƒdttddƒtdƒd  tdtdƒ d ƒd  ƒ dttddƒtdƒd  tdtdƒ d ƒd  ƒ dttdƒ d tj	 tddtdƒ  ƒd  ƒ dttddtdƒ  ƒ d tdƒd  tj	 ƒ gkszJ ‚d S )Nr   ©Úsechrs   r“   rt   ry   )
Úsympyr  r+   r*   rd   r   r   r-   r   r«   r  ro   ro   rp   Útest_rewrite_trigh2  s   4422ür  c                  C   s  t ttƒ tttdtd td     ƒ } t| tddttttt ƒ  ƒ ttttt ƒ  ƒgks4J ‚tttd ƒtddt  ƒ d ƒdtdtdƒ ƒttddƒƒ d  tdƒd  tdtdƒ ƒ ttddƒƒ d d tdƒd  gdtd	tdƒ d
 d  ƒd  tdƒd  dtd	tdƒ d
 d  ƒd  tdƒd  gfv s©J ‚tttdt ƒd ƒtttƒ d ƒ tdƒ ƒg ksÆJ ‚d S )Nr“   rs   T)Zforceru   rx   r‰   iôÿÿÿiÜÿÿÿrŠ   )	rf   r%   rd   re   r+   r-   r#   r   r2   rQ  ro   ro   rp   Útest_uselogcombine=  s   ,<"02ÿ,,ÿ
ý>r	  c                   C   s.   t ttdƒtd  tƒdtdƒ gksJ ‚d S r[  )r+   r4   rd   r&   r-   ro   ro   ro   rp   Ú
test_atan2I  s   .r
  c                   C   s„   t ttƒt tƒttƒgksJ ‚t ttƒt tƒttƒgks J ‚t ttƒt tƒttƒgks0J ‚t ttƒt tƒttƒgks@J ‚d S r‹   )r+   r   rd   re   r    r!   r"   ro   ro   ro   rp   Útest_errorinversesM  ó      $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 )Nrj   rs   rx   TrŸ   rt   ru   r“   éû   r·   éo   r/  rö   )r   r-   r+   r   r
   )rj   r€   rÒ   ro   ro   rp   Útest_issue_2725T  s,   @*ÿÿ$ÿÿÿÿÿ"ÿþr  c                  C   sf  t dƒ\} }}}}}}}}}	}
}}}}}}t| ||  ||  g|d| d|  d|   ||  ||  g| | |d| d|  d|    ||  g| | |d| d|
  d|    |	|  g| | |	d| d|  d|    ||  g|	 | |d| d|    ggƒ}t|||	|| |gƒ}tt|ƒt|ƒdd}tdd„ | ¡ D ƒƒdks±J ‚d S )Nzb:rrx   Fr˜   c                 S   s   g | ]}|  ¡ ‘qS ro   )Ú	count_ops)r   rÆ   ro   ro   rp   rå   l  ó    z(test_issue_5114_6611.<locals>.<listcomp>iÆ  )r/   r   r+   r¢   rè   ré  )r]   r^   r_   r`   r{   r|   rb   rÏ   r·  ra   r¸  ri   rm   rä   rc   rh   rÇ   r‘   rË  r   ro   ro   rp   Útest_issue_5114_6611^  s   *@\Lý"r  c                  C   s    t ddtdƒƒ} |  ¡ t| ƒksJ ‚d| d< |  ¡ t| ƒks J ‚t ddttdƒƒƒ} |  ¡ t| ƒks4J ‚tdddƒ}t|ƒt|ƒ  krK| ¡ ksNJ ‚ J ‚d S )Nru   za:9rx   rq  r/  rs   )rx   rs   rx   rƒ   )	r   r/   ZdetrO   r¢   rê   r7   rP   rQ   )ri   rÆ   ro   ro   rp   Útest_det_quicko  s   ,r  c                  C   s’   t ddd\} }tt| d |d  ƒd | ƒt|d  d ƒ t|d  d ƒgks,J ‚t ddd\} }tt| d |d  ƒd | ƒg ksGJ ‚d S )Nza bTrâ   rs   ru   r/  r÷  rå  rK  ro   ro   rp   Útest_real_imag_splitting{  s   $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 )Nry   ru   rƒ   rs   rt   c                 s   s    | ]
}t t |¡ƒV  qd S r‹   )r8   r   rã   rÎ   ro   ro   rp   r’   …  r©  z"test_issue_7110.<locals>.<genexpr>)rd   r­  r+   rË   ro   ro   rp   Útest_issue_7110ƒ  s   $r  c                   C   s*   t dt ddt   ƒdt gksJ ‚d S rS  )r+   rd   rT   ro   ro   ro   rp   Ú
test_unitsˆ  r  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@ró   r   g    d6 Ag    0Œ!A)r   r   r   z4442890172.68209z4289299466.1432z70.5389666628177)r/   r   r   r:   r9   ra  )ri  rj  ÚVÚeq1Úeq2Úeq3rÒ   ro   ro   rp   Útest_issue_7547Œ  s   &
þÿr  c                  C   s*   t ddd} tt| ƒd ƒdgksJ ‚d S )NrÇ   Trâ   rs   rƒ   rå  )rÇ   ro   ro   rp   Útest_issue_7895˜  rá  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 )Nrö  Trâ   rs   r‡   ru   é¿   r¿   i‡  rŠ   Fr½   )r/   r-   r   r+   )rd   re   rØ  rÙ  r\   r]   r   ro   ro   rp   Útest_issue_2777  s   8""r  c                  C   s"   d} t t|  tƒd | ksJ ‚d S )Ng{[Rs±Ò8r   r´   )Znumberro   ro   rp   Útest_issue_7322«  s   r  c                   C   s.   t tdd„ ƒ t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t tdddS )N)r“   rx   Zbisect)Úmethod)r:   rd   ro   ro   ro   rp   rœ   ±  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 )Nru   )iÎÿÿÿrô   )r:   rd   re   rf   ro   ro   ro   rp   rœ   ²  s   ( c                   S   s   t tt tt fdƒS )Nrn  )r:   rd   re   ro   ro   ro   rp   rœ   ³  rw  )rZ   r`  r~   ro   ro   ro   rp   Útest_nsolve°  s   r!  c                      sæ   t tttd  t d tƒƒdksJ ‚t tttd  t d tƒƒdk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 )
Nru   rx   rƒ   rt   c                   S   s   t ttd  t d tddS )Nrt   rx   F)Z
incomplete)r+   r\   rd   ro   ro   ro   rp   rœ   »  rr   z.test_high_order_multivariate.<locals>.<lambda>c                    s   g | ]	}t ˆ d  |ƒ‘qS rC  rU   rÎ   ©r_   ro   rp   rå   Á  rU  z0test_high_order_multivariate.<locals>.<listcomp>rs   )	rÑ   r+   r\   rd   rZ   r   rê   r   r«   ro   ro   r"  rp   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   rx   rs   zx*(1/x**0 - x)F©Zevaluate)r+   rd   r   ro   ro   ro   rp   Útest_base_0_exp_0Æ  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 )Nrx   r   ru   )rR   rd   r–   re   r3   ro   ro   ro   rp   Útest__simple_densÍ  s   "$r&  c                   C   s”   t tttƒt td  d tƒƒdksJ ‚t tdtd  dtd tddƒ  td   dtd tddƒ  t  dt  d td	d
ƒdksHJ ‚d S )Nru   rx   r¢  r£  rs   r¤  rš  r¥  Fr¦  )rÑ   r+   r-   re   rd   r   ro   ro   ro   rp   Útest_issue_8755Ó  s   *,ÿÿÿÿÿr'  c                  C   sN  d} d}d}d}d}d}d}d}t ttf}t |  d	 t| d	  |t d	  }	|t  d	 |t d	  td	  }
t | d	 t| d	  |t d	  }|	|
|f}tt |  d	 t| d	  ƒt | }|
}tt | d	 t| d	  ƒt | }|||f}t||ƒ}t||ƒ}t||d
d}dd„ |||fD ƒ\}}}||  kr¢|ks¥J ‚ J ‚d S )Nr   i”ýÿÿi˜  é~   r   r6  éÍ   éh   rs   Trî  c                 S   s   g | ]	}d d„ |D ƒ‘qS )c                 S   s   h | ]}t d d„ |D ƒƒ’qS )c                 s   s    | ]}|  d ¡V  qdS )rs   N)rl   rÎ   ro   ro   rp   r’   ö  rÐ   z7test_issue_8828.<locals>.<listcomp>.<setcomp>.<genexpr>)r¡   )r   r·  ro   ro   rp   Ú	<setcomp>ö  rW  z-test_issue_8828.<locals>.<listcomp>.<setcomp>ro   )r   rj   ro   ro   rp   rå   ö  rU  z#test_issue_8828.<locals>.<listcomp>)rd   re   rf   r-   r+   )rí   Zy1Zr1rE  Zy2rF  Zy3Zr3rË  Úf1Úf2Zf3re  Zg1Zg2Zg3rÐ  ri  rj  rk  rc   rh   rÇ   ro   ro   rp   Útest_issue_8828Ü  s,   
$ $
$$


 r.  c                   C   sú  t tdt ƒtdt ƒ ƒdttddƒ ttddƒ t ttddƒ ttddƒ t d ttddƒ ttddƒ td ttd	dƒ ttddƒ tttd	dƒ ttd
dƒ ttddƒ ttddƒ dt dt tdtddƒ  ƒ dt tdtddƒ  ƒ dt tttd ƒ tttd ƒ  ƒ dt tttd ƒ tttd ƒ  ƒ dt tttd ƒtttd ƒ  ƒ dt tttd ƒtttd ƒ  ƒ gksÐJ ‚t dttƒ dtdt ƒ  ƒdttddƒ t t d td tttddƒ gksûJ ‚d S )Nru   rŠ   r   r  rL  ry   r/  rs   rƒ   rB  rt   r›   r“   rx   r(  )r+   r)   rd   r&   r   r
   r%   r   ro   ro   ro   rp   Útest_issue_2840_8155ú  s   *,,*4((&&
÷
.ÿr/  c                   C   s"   t ddtd   ƒdgksJ ‚d S r’  r´   ro   ro   ro   rp   Útest_issue_9567
  s   "r0  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 )Nrs   ru   rƒ   rL  ry   )r+   rd   r<   r
   r-   r=   re   rÑ   r×  ro   ro   rp   Útest_issue_11538  s   .22
ý*
ÿ r1  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 ƒ |||||di| t|d  d ƒ|t|d  d ƒ|t|d  d ƒ|||||di| tdƒ | d t|d  d ƒd  |tdƒ| d t|d  d ƒd  |t|d  d ƒ|| d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |di| tdƒ | d t|d  d ƒd  |tdƒ| d t|d  d ƒd  |t|d  d ƒ || d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |di| tdƒ| d t|d  d ƒd  |tdƒ | d t|d  d ƒd  |t|d  d ƒ|| d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |di| tdƒ| d t|d  d ƒd  |tdƒ | d t|d  d ƒd  |t|d  d ƒ || d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |digksJ ‚d S )
Nza,b,c,d,e,f,grx   rs   Trv   r“   ru   r‰   rŠ   rå  )	r\   r]   r^   r_   r`   r{   r|   ZtermsrÆ   ro   ro   rp   Útest_issue_12114  s@   66ÿ* ÿ$ÿ(8",ý(:",ý&:",ý&<",ýðr2  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$J ‚d S rX  )r+   r;   rd   ro   ro   ro   rp   Útest_inf:  s   r3  c                     sò   t dƒ‰‡fdd„tdƒD ƒ} tdƒ}tt| |ƒƒ}|d d… |dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}| d d… | dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}|| d	   |¡ ¡ ||d	   ¡ kswJ ‚d S )
Nr{   c                    s   g | ]}ˆ |ƒ‘qS ro   ro   rÎ   rT  ro   rp   rå   B  r  z$test_issue_12448.<locals>.<listcomp>rk   zx:15ru   c                    óT   g | ]&}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS ©rƒ   rx   rs   ru   ro   rÎ   ©r^   rd   re   rf   ro   rp   rå   G  ó    Lÿc                    r4  r5  ro   rÎ   r6  ro   rp   rå   K  r7  r   )r   rê   r/   rw   r—  r+   Zxreplacer  )Zfunr‰  r˜  ZssymZsfunro   )r^   r{   rd   re   rf   rp   Útest_issue_12448@  s&    ÿÿ ÿÿÿr8  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 )Nrs   rx   )rS   rd   re   rf   ro   ro   ro   rp   Útest_denomsR  s     ".,2r9  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 x5rs   ru   rŠ   rx   ry   r“   r   rt   )r/   r   r   r«   r-   r+   )rì   rí   rE  rF  rG  rH  rd  Zsolsro   ro   rp   Útest_issue_12476[  s   J
ÿÿÿþþ
þ
þý0ý0üü
û
ûû0ú0ù ùø
øøø 	÷	÷	÷
	÷

ö

ö
ö
ö
ö
ö2"288ûr:  c                  C   s:   t dƒ} t| tdƒtdƒ  tdƒ | f| ƒg ksJ ‚d S )Nrg   rt   rs   rå  )rg   ro   ro   rp   Útest_issue_13849r  s   2r;  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kilorØ   iÀàÿÿ)Úsympy.physics.unitsr=  r>  r+   rd   re   r<  ro   ro   rp   Útest_issue_14860w  s   0r@  c               	   C   sb  t dƒ\} }}}td|  d d |d   | d d |d   d|  d d |d   | d d |d   || d g|| ||ƒdd| td|d d  ƒ |fdd|td|d d  ƒ |fgkseJ ‚t||| d|d   d | d d|d   d g|||ƒ|dtdƒ d f|dtdƒd fgks™J ‚t||d  d ||d  d fƒg ks¯J ‚d S )Nz:4r“   rx   rs   r   ry   r/  rå  )ra   rb   r\   r]   ro   ro   rp   Útest_issue_14721|  s*   ..ýý þý0ÿÿ"ÿÿ0rA  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 )
Nrd   Trâ   rƒ   é‚   rs   iA  i  rø   )r/   r+   r-   r   rÖ   ro   ro   rp   Útest_issue_14779Š  s   0ÿÿÿÿrC  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 )Nrs   ru   Fr$  r‰   rƒ   r“   iá0  iÕW i¢éÿÿry   rØ   rö   rš   r3  )r+   re   r6   rd   r?   r   )r  r  ro   ro   rp   Útest_issue_15307  s    ÿ
ÿ 
ÿ" rD  c                   C   sÔ   t td tƒdgksJ ‚t td gtƒtdiksJ ‚t ttdtd  d  tdt  ƒtƒg ks2J ‚t ttdtd  d  tdt  ƒgtƒg ksKJ ‚t ttdtd  d  tdt  ƒttdƒgtƒg kshJ ‚d S )Nru   rs   rx   )r+   rd   r   re   ro   ro   ro   rp   Útest_issue_15415œ  s
   02>rE  c                  C   sú  t ttd dt  d td dt  d  dƒƒg d¢ksJ ‚t ttd  d ƒd	gks.J ‚t t t d  d ƒdgks?J ‚t td d
 td d  d ƒd	dgksUJ ‚t td dt  d td d  dddtdƒ    ƒtdƒgksxJ ‚t tttj  dtdƒ  ƒtdƒgksŽJ ‚t td d t d ƒdgksŸJ ‚t tdt  d ƒddgks¯J ‚t td dt  tdƒ ƒddgksÃJ ‚t tttj  tddƒ ƒtddƒgksÙJ ‚t ttdƒƒ t d ƒdtdƒtdtddƒ ƒtt	   gksûJ ‚t tdƒt ttdƒƒ ƒtjgksJ ‚t tdƒ t dtdƒ  ƒddtdƒd  dt	d   dt t	 tdƒ  tdƒd dt	d    gksHJ ‚t tdƒt dtdƒ  ƒdgks\J ‚t tt d ƒdgksjJ ‚t dt t dt  ƒdgks|J ‚t tdƒtdƒ t dtd
ƒ d tddƒ  ƒtddƒgksžJ ‚t
dƒ} t | t | d  tƒdgks³J ‚t | t d|   tƒdgksÄJ ‚t | t |  tƒdgksÓJ ‚t
ddd} t | t | d  tƒdgksêJ ‚t | t d|   tƒdgksûJ ‚d S )Nrs   rÀ   rû   r  r•   rx   )rs   ru   rƒ   rt   rŠ   rÀ   rƒ   ry   rŠ   ru   r  rØ   r/  rt   r]   r“   Trz  )r+   r   rd   r-   r   r«   r   r%   r
   r&   r   )r]   ro   ro   rp   Útest_issue_15731¤  s4   >",F," (,D*Fÿ($D"""&rF  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 )Nrƒ   rÒ  ru   rs   rÛ  )r+   rd   re   r
   ro   ro   ro   rp   Útest_issue_10933Ä  s   ,rG  c                  C   s,   t ddd} tt| t ƒ| ƒdgksJ ‚d S )Nrd   Trâ   r   )r/   r+   rø  re   rÖ   ro   ro   rp   Útest_Abs_handlingÉ  s    rH  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 )Nrd   rs   rt   r¿   r   g      ø?ru   g)\Âõ( @g=
×£p=L@éj   rx   )r   r+   r   ZfalserÖ   ro   ro   rp   Útest_issue_7982Î  s   4JrJ  c                  C   sP   t dƒ\} }t| | |  | | | |  | g| |gƒ||d  |fgks&J ‚d S )Nrö  rx   r¾  rÿ  ro   ro   rp   Útest_issue_14645Ö  s   DrK  c                  C   sR   t dƒ\} }ttd| dk f| | dkfƒ| ƒ|td| dk f| dfƒigks'J ‚d S )Nrö  rž   rÒ  T)r/   r+   r@   rÿ  ro   ro   rp   Útest_issue_12024Û  s    ÿrL  c                   C   s¬   t dt t t tƒtttƒtt  ƒ ttdƒƒ tttƒtt  ƒttdƒƒ gks.J ‚t ttd  td  tƒttdtdƒ dttƒ  dt t  ƒƒgksTJ ‚d S )NrÀ   rû   iõÿÿÿ)r+   rd   r&   r-   r%   r
   r#   r   ro   ro   ro   rp   Útest_issue_17452á  s   4
ÿPrM  c                   C   s0   t tttdƒd  ƒt  t tƒg ksJ ‚d S r  )r+   r   rd   r   r&   r
   ro   ro   ro   rp   Útest_issue_17799ç  rÛ   rN  c                  C   sN   t ddd} ttt| d d ƒ|  ƒ|  ƒddtdƒ dtdƒ gks%J ‚d S )Nrd   Trâ   rs   rx   r“   )r   r+   rø  r-   rÖ   ro   ro   rp   Útest_issue_17650ë  s   BrO  c                  C   s\   dt d  dt d d tdƒd    ddt d d tdƒd     } t| ƒd u s,J ‚d S )Niøÿÿÿrs   r/  rx   rƒ   ru   )rd   r   rK   rQ  ro   ro   rp   Útest_issue_17882ð  s   HrP  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 rV  )r+   r#   rd   ro   ro   ro   rp   Útest_issue_17949õ  r  rQ  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 )Nrs   ru   ry   )rL  r   rx   r   rx   )ry   r“   ru   )r+   r   r   rd   Úpowr\   re   r)   ro   ro   ro   rp   Útest_issue_10993ü  s    * &J,rS  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 )Nrx   r“   rs   ry   )rd   re   rA   r+   rB   )r  r  r  ro   ro   rp   Útest_issue_11553	  s
   &,rT  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 )Nrx   ru   rt   rƒ   rs   ry   )	r   r+   r   rd   r)   r   r-   r
   r«   )rg   rb   ro   ro   rp   Útest_issue_19113_19102	  s   "* 
þ4244
ü*rU  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 )Nru   rƒ   rt   rØ   rx   rs   )r   r-   r+   rd   ©r\   r]   r^   r_   ro   ro   rp   Útest_issue_19509	  s   ürW  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 c4rx   )r/   r#   r%   r+   )ZTHTZHTZDBHZdibZc0Zc1Zc2Zc3Zc4r{   Zrhsr€   ZtermrÒ   ro   ro   rp   Útest_issue_20747'	  s   (*ÿ"rX  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 )
Nrx   rs   ru   r   r“   rL  ry   rƒ   r  )rg   r+   rÂ   rd   r   r   rT  ro   ro   rp   Útest_issue_209021	  s
   FJFJrY  c               	   C   sÄ   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tdƒƒttttdƒƒƒttt| ƒƒiks:J ‚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\   Trâ   rƒ   rt   )
r/   rd   r   r   re   r*   rf   r2   r+   r#   )r\   ru  Z	newsystemro   ro   rp   Útest_issue_210349	  s   *(
ÿ6rZ  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 rV  )r\   r-   rj   r]   r^   r+   rd   re   )rf   rg   rÒ   ro   ro   rp   Útest_issue_4886E	  s   @<@r[  c                  C   sT   t ddd\} }}}t| |t  ||t   tƒt||  ƒt|| ƒ gks(J ‚d S )Nrh  Trz  )r/   r+   rd   r%   rV  ro   ro   rp   Útest_issue_6819L	  s   @r\  c                  C   sB   ddt dƒ d  g} tdt t dtd  ƒ d ƒ| ksJ ‚d S )Nr#  rs   )r-   r+   rd   )r²   ro   ro   rp   Útest_issue_21852Q	  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t  tttt    t dt  t  ddt   gksDJ ‚d S )Nrx   Fr¨  )r_   r\   r^   r`   r]   r+   rò  ro   ro   rp   Útest_issue_21942V	  s   6Fr^  N)rk   )úr  r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   Zsympy.core.functionrC   Zsympy.solversrD   rE   rF   Zsympy.solvers.bivariaterG   rH   rI   Zsympy.solvers.solversrJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   r?  rT   Zsympy.polys.rootoftoolsrV   Zsympy.testing.pytestrW   rX   rY   rZ   Zsympy.testing.randtestr[   rÃ   r^  r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rq   r}   r‚   r„   r…   r†   rˆ   r§   r³   rµ   r¸   r¹   rº   rÉ   rÊ   rÌ   rÓ   rÔ   rÕ   r×   rÙ   rÚ   rÜ   rÞ   rà   rá   rð   rI  rJ  rc  rf  rg  rl  rs  rt  rv  ry  r}  r  r€  r  r‚  rŠ  rŒ  r  rŽ  r°  r±  r²  r´  rµ  r¶  r¹  rÌ  rÍ  rÎ  rÑ  rÖ  rß  rà  râ  rã  ræ  rè  rë  rì  rí  rï  rð  rñ  ró  rô  rõ  rù  rþ  r   r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r!  r#  r%  r&  r'  r.  r/  r0  r1  r2  r3  r8  r9  r:  r;  r@  rA  rC  rD  rE  rF  rG  rH  rJ  rK  rL  rM  rN  rO  rP  rQ  rS  rT  rU  rW  rX  rY  rZ  r[  r\  r]  r^  ro   ro   ro   rp   Ú<module>   sF  þ  	0D
O$


7
o3'-
,


  2


*C	(	
1

N



	


	

	
