o
    Ðe$˜ ã                   @   s‚  d dl mZmZ d dlmZ d dlmZ d dlmZm	Z	m
Z
 d dlmZ d dlmZmZ d dlmZmZmZmZmZmZ d dlmZmZmZmZ d d	lmZ d d
lmZm Z m!Z!m"Z" d dl#m$Z$ d dl%m&Z& d dl'm(Z(m)Z)m*Z*m+Z+m,Z, d dl-m.Z.m/Z/m0Z0 d dl1m2Z2m3Z3m4Z4m5Z5 d dl6m7Z7m8Z8m9Z9 d dl:m;Z; d dl<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZD d dlEmFZFmGZGmHZHmIZI d dlJmKZK d dlLmMZMmNZN d dlOmPZP d dlQmRZR d dlSmTZT d dlUmVZV d dlWmXZX d dlYmZZZm[Z[m\Z\ d dlm]Z] d dl^m_Z_m`Z`maZa d dlbmcZcmdZdmeZe d dlYmfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZo d d lpmqZq d d!lrmsZs d d"ltmuZumvZvmwZwmxZx d d#lymzZ{ d d$l|m}Z}m~Z~mZm€Z€mZm‚Z‚mƒZƒm„Z„m…Z…m†Z†m‡Z‡mˆZˆm‰Z‰mŠZŠm‹Z‹ dNd&d'„ZŒd(d)„ Zd*d+„ ZŽd,d-„ Zd.d/„ Zd0d1„ Z‘d2d3„ Z’d4d5„ Z“d6d7„ Z”d8d9„ Z•d:d;„ Z–d<d=„ Z—d>d?„ Z˜d@dA„ Z™dBdC„ ZšdDdE„ Z›dFdG„ ZœdHdI„ ZdJdK„ ZždLdM„ ZŸdNdO„ Z dPdQ„ Z¡dRdS„ Z¢dTdU„ Z£dVdW„ Z¤dXdY„ Z¥evdZd[„ ƒZ¦d\d]„ Z§d^d_„ Z¨d`da„ Z©dbdc„ Zªeuddde„ ƒZ«dfdg„ Z¬dhdi„ Z­djdk„ Z®dldm„ Z¯dndo„ Z°dpdq„ Z±drds„ Z²dtdu„ Z³dvdw„ Z´dxdy„ Zµdzd{„ Z¶d|d}„ Z·d~d„ Z¸ewd€ƒdd‚„ ƒZ¹dƒd„„ Zºd…d†„ Z»d‡dˆ„ Z¼evd‰dŠ„ ƒZ½d‹dŒ„ Z¾euddŽ„ ƒZ¿eudd„ ƒZÀevd‘d’„ ƒZÁd“d”„ ZÂd•d–„ ZÃd—d˜„ ZÄeud™dš„ ƒZÅd›dœ„ ZÆddž„ ZÇdŸd „ ZÈd¡d¢„ ZÉd£d¤„ ZÊd¥d¦„ ZËd§d¨„ ZÌd©dª„ ZÍd«d¬„ ZÎd­d®„ ZÏd¯d°„ ZÐd±d²„ ZÑd³d´„ ZÒdµd¶„ ZÓd·d¸„ ZÔd¹dº„ ZÕd»d¼„ ZÖd½d¾„ Z×d¿dÀ„ ZØdÁdÂ„ ZÙdÃdÄ„ ZÚdÅdÆ„ ZÛdÇdÈ„ ZÜdÉdÊ„ ZÝevdËdÌ„ ƒZÞeudÍdÎ„ ƒZßdÏdÐ„ ZàevdÑdÒ„ ƒZádÓdÔ„ ZâdÕdÖ„ Zãd×dØ„ ZädÙdÚ„ ZådÛdÜ„ ZædÝdÞ„ Zçdßdà„ Zèdádâ„ Zédãdä„ Zêdådæ„ Zëdçdè„ Zìdédê„ Zídëdì„ Zîdídî„ Zïeudïdð„ ƒZðdñdò„ Zñdódô„ Zòdõdö„ Zóeud÷dø„ ƒZôeudùdú„ ƒZõdûdü„ Zödýdþ„ Z÷eudÿd „ ƒZødd„ Zùdd„ Zúdd„ Zûdd„ Züd	d
„ Zýdd„ Zþdd„ Zÿdd„ Z dd„ Zdd„ Zeudd„ ƒZdd„ Zdd„ Zdd„ Zdd„ Zdd „ Zd!d"„ Z	d#d$„ Z
d%d&„ Zd'd(„ Zd)d*„ Zd+d,„ Zd-d.„ Zd/d0„ Zd1d2„ Zd3d4„ Zd5d6„ Zd7d8„ Zd9d:„ Zd;d<„ Zd=d>„ Zd?d@„ ZdAdB„ ZdCdD„ ZdEdF„ ZdGdH„ ZdIdJ„ ZdKdL„ ZdMS (O  é    )ÚQÚask)ÚAdd)ÚTuple)Ú
DerivativeÚFunctionÚdiff)ÚMul)ÚGoldenRatioÚTribonacciConstant)ÚEÚFloatÚIÚRationalÚooÚpi)ÚEqÚGtÚLtÚNe)ÚS)ÚDummyÚSymbolÚWildÚsymbols)Úsympify)Úbinomial)ÚAbsÚargÚ	conjugateÚimÚre)ÚLambertWÚexpÚlog)ÚatanhÚcoshÚsinhÚtanh)ÚcbrtÚrootÚsqrt)Ú	Piecewise)ÚacosÚasinÚatanÚatan2ÚcosÚsecÚsinÚtan)ÚerfÚerfcÚerfcinvÚerfinv)ÚIntegral)ÚAndÚOr)ÚMatrix)ÚSparseMatrix)ÚPoly)Ússtr)Údenom)ÚnsolveÚsolveÚsolve_linear)Únfloat)Úsolve_linear_systemÚsolve_linear_system_LUÚsolve_undetermined_coeffs)Ú_filtered_gensÚ_solve_lambertÚ_lambert)
Ú_invertÚunradÚchecksolÚposifyÚ_ispowÚ	det_quickÚdet_permÚ	det_minorÚ_simple_densÚdenoms)Úcm©ÚCRootOf)ÚslowÚXFAILÚSKIPÚraises)Úverify_numerically)ÚaÚbÚcÚdÚeÚkÚhÚpÚxÚyÚzÚtÚqÚmÚRé   c                 K   s   t t| ƒj|fi |¤ŽddS )NT)Z	full_prec)r?   r   Úevalf)ra   ÚnÚoptions© rp   úPD:\Projects\ConvertPro\env\Lib\site-packages\sympy/solvers/tests/test_solvers.pyÚNS-   ó   rr   c                  C   sö   t tdƒ\} }| tƒ|tƒ}}t|t d || d g|t|ƒ||d t| d iks.J ‚t||t  d ||gdd|d|digksFJ ‚t||d t  t ||gdd|t|digks`J ‚t| dƒd td gddtd	| dƒdigksyJ ‚d S )
NZfgé   é   é   T©Údictr   é   éþÿÿÿ)Úmapr   re   rB   rf   )ÚfÚgZfxZgxrp   rp   rq   Útest_swap_back1   s    ÿ046r~   c              	   C   s*   zt | |ƒ W dS  ttfy   Y dS w )NTF)rB   Ú	TypeErrorÚNotImplementedError)ÚeqÚsymbolrp   rp   rq   Úguess_solve_strategy;   s   
ÿrƒ   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   rt   ry   rv   )rƒ   r   re   r]   r+   r   rf   r#   rp   rp   rp   rq   Útest_guess_polyC   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 )Nry   rv   r„   )rƒ   r+   re   r   rf   rp   rp   rp   rq   Útest_guess_poly_cvS   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 )Nry   rt   rv   )rƒ   re   rf   r+   r   rp   rp   rp   rq   Útest_guess_rational_cv^   s
   $ÿ4r‡   c                   C   sœ   t ttƒd tƒsJ ‚t dttƒ t tƒsJ ‚t ttƒtt ƒ t tƒs(J ‚t dt d tƒs3J ‚t dt  d tƒs?J ‚t ttt  t tƒsLJ ‚d S )Nry   rt   rv   é
   )rƒ   r#   re   r1   rf   r]   r^   rp   rp   rp   rq   Útest_guess_transcendentali   s   ÿr‰   c               	      sF	  t dtdi‰ t dt  d dt  dt  d f‰t‡ ‡fdd„ttttfD ƒƒs*J ‚ttˆŽ t tƒˆ ks6J ‚ttt d d	 ƒƒt	dƒt	dƒ hksKJ ‚tt t d
 t t d gƒt d	tdiksaJ ‚tt t
t ƒ t ddt
t ƒgkssJ ‚tdƒtdt ƒ  krƒg ks†J ‚ J ‚tddgƒg ksJ ‚ttdƒgt gƒg ksJ ‚ttdd„ ƒ ttdd„ ƒ tt t ttgddgks¹J ‚ttdd„ ƒ ttdd„ ƒ tt t ttgddgksÕJ ‚ttd
 thƒd
gksâJ ‚ttd
 t thƒtd
igksòJ ‚tt t d
 t tgƒd
t tfgksJ ‚tt t d
 t tgddt d
t igksJ ‚tt t d
 ƒt d
t igks0J ‚tttt   d ttgƒtdtdiksFJ ‚ttt t  t t ttgƒtt ttiks_J ‚tt d  tt   t t t d d	t t  d	 t  } t| tttgtttgd}|tt dt  td	t t td  d	t  tdd	t  iksªJ ‚t| tttgdd|gksºJ ‚t| tttgddtttgt dt  dd	t  d	t t td  d	t  fhfksçJ ‚t| tttgtttgddtt dt  td	t t td  d	t  tdd	t  iksJ ‚tt t  td  d ttf}t|Ž td tt   d t  tfgks:J ‚ttt  td t d	   d
t   d	t   ttddttd  t  d
t d
   dt d   d	t   d t d t d	   igks{J ‚tddt  t t
tƒ  ƒg ksŽJ ‚ttdd„ ƒ ttt
t ƒt  gƒt tdƒ tdigks¬J ‚tt
t ƒt  t
tƒt fƒt tdƒ ttdƒ igksÊJ ‚ttt
t ƒt  gt tƒtdƒ dfgksáJ ‚tt d t tƒt d gksòJ ‚tg t gƒg ksýJ ‚tt d d	 td ft tƒddgksJ ‚tt d d	 td ftt ƒddgks'J ‚tt d d	 t td t ftttt ddtttt gtttd td	t ƒ ftttd td	t ƒfhfks_J ‚tt t d d	 t t d gƒt t d igkszJ ‚tt t d dt  dt  d	 fƒt t d iks–J ‚ttt d d ƒƒd gks¥J ‚tdtt dƒgt gddt digksºJ ‚ttt t ƒtt dƒtt t d ƒgt gddg ksÕJ ‚ttt t d ƒt dk gt ƒræJ ‚ttt dƒt d dk gƒtt dƒksûJ ‚ttt t ƒtt t d ƒgt ƒg ksJ ‚tdt ƒg ksJ ‚tt d dgt gddg tƒ fks-J ‚tt t t d  d td t  t dt  gddd!t tgdt tft dfhfksZJ ‚tttd t td
ƒt  fƒ ¡ ƒt tgkssJ ‚tt d t gtt fddtt gtƒ fksŠJ ‚tt d t gtt hddt tgtƒ fks¡J ‚d S )"Néýÿÿÿry   ru   rt   é   rl   c                 3   s$    | ]}t |ˆƒttƒˆ kV  qd S ©N©rB   re   rf   )Ú.0Ú	container©ÚansÚeqsrp   rq   Ú	<genexpr>y   s   €" z"test_solve_args.<locals>.<genexpr>r„   rv   éÿÿÿÿT©Zimplicité*   c                   S   ó   t td td ftttƒS ©Nrv   rt   r   rp   rp   rp   rq   Ú<lambda>…   ó    z!test_solve_args.<locals>.<lambda>c                   S   ó   t tttƒS rŒ   ©rB   re   rp   rp   rp   rq   r™   †   ó    ©Úexcluder   c                   S   r—   r˜   r   rp   rp   rp   rq   r™   Š   rš   c                   S   r›   rŒ   rœ   rp   rp   rp   rq   r™   ‹   r   rw   ©ÚsetF)rŸ   Úsimplifyé   é   c                   S   s$   t ttƒttƒ ttƒ ttƒ ƒS rŒ   )rB   r#   re   r3   rf   rp   rp   rp   rq   r™   ±   ó   $ )rz   rt   )rt   rt   )rt   rz   ç        )r¡   Úcheck)re   rf   ÚallÚtupleÚlistr¡   Ú	frozensetrB   r   r   r#   r+   r[   Ú
ValueErrorr]   r^   r_   rc   rd   rb   r€   r"   r   rg   r   Úkeys)r   ÚsolÚargsrp   r   rq   Útest_solve_argsu   sž   $
ÿ*,$& *.$,28D >
ÿ8
ÿ,2F
ÿ&ÿ.ÿ
ÿ."***
þ
ÿ68*6"*((.ÿ
ÿ2.2r°   c                  C   sÆ  t dt d tƒtddƒgksJ ‚t tdt dƒtƒtddƒgks#J ‚tt td d tƒƒtj tjhks7J ‚tt ttd dƒtƒƒtj tjhksLJ ‚t ttd  tƒtd gks\J ‚ttdƒ} t ttd  tƒ| |  d t	dƒt
 |  d  |  d t	dƒt
 |  d  gks‹J ‚tdƒ\}}}}}}t |t |t  | |t |t  | gttƒt|| ||  || ||   t|| ||  || ||   iksÑJ ‚ttjttji}t tt tt fttƒ|kséJ ‚t tt tt fttfƒ|ksúJ ‚t tt tt fttgƒ|ksJ ‚tt td dt  d tƒƒddtj  tdƒddtj  hks/J ‚tt td d d t tƒƒt	dt	tƒ ƒt	dt	tƒ ƒ t	dt	tƒ ƒt	dt	tƒ ƒ hksaJ ‚d S )Nrv   rt   ry   úa11,a12,a21,a22,b1,b2rl   r„   rz   )rB   re   r   r   r¡   r   ÚOnerf   r*   r+   r   r   ÚZeroÚHalfr]   )ÚrxÚa11Úa12Úa21Úa22Úb1Úb2Úsolutionrp   rp   rq   Útest_solve_polynomial1Ý   s:   "$(* 
:
ÿ.  þÿ "$ýÿÿr½   c                   C   s   t dtƒg ks	J ‚d S )Nr„   rœ   rp   rp   rp   rq   Útest_solve_polynomial2  ó   r¾   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)
    ry   rt   r„   r¤   rv   é   r   N)rB   r+   re   r   rp   rp   rp   rq   Útest_solve_polynomial_cv_1a  s
   ""8rÁ   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 )Nr„   ry   rt   rv   rÀ   )r¡   rB   re   r]   r+   r   r³   r*   rp   rp   rp   rq   Útest_solve_polynomial_cv_1b  s   82rÂ   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
    ry   rv   rt   N)rB   re   r   r´   r   r+   rp   rp   rp   rq   Útest_solve_polynomial_cv_2  s
   **ÿÿrÃ   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 )Nru   én   rv   é7   rt   i	  iÓ  F©r§   r   rl   rˆ   é   é   ©Úexponent)re   rB   Úsubsrn   ÚtnÚfuncrW   rD   ©r|   ÚsÚrÚresrp   rp   rq   Útest_quintics_1   s   ,,&	 ÿrÒ   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 )Nru   rl   r£   FrÆ   r   rv   rt   rˆ   rÇ   r‹   ry   r„   )re   rB   rË   rn   rÌ   rÍ   rW   rÎ   rp   rp   rq   Útest_quintics_27  s    ,*,,,,,ûrÓ   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 )Nru   rv   rt   ry   )re   r   rB   ©rf   rp   rp   rq   Útest_quintics_3K  s   *rÕ   c                  C   s>   t td dt  d ƒ} tdd„ | D ƒƒrt| ƒdksJ ‚d S )Nr‹   rt   c                 s   s    | ]}t |tƒV  qd S rŒ   )Ú
isinstancerW   ©rŽ   Úirp   rp   rq   r“   S  ó   € z&test_highorder_poly.<locals>.<genexpr>)rB   re   r¨   Úlen©r®   rp   rp   rq   Útest_highorder_polyP  s   &rÜ   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 functionsrv   rt   ry   N)rB   re   rf   r+   rp   rp   rp   rq   Útest_solve_rationalV  s   <rÝ   c                   C   s&   t ttƒd t ƒdt gksJ ‚dS )z)Test solve for simple conjugate functionsrv   N)rB   r   re   r   rp   rp   rp   rq   Útest_solve_conjugate[  s   &rÞ   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 )Nrt   Trw   )rB   re   rf   r#   r+   rp   rp   rp   rq   Útest_solve_nonlinear`  s   26ÿrß   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 )Nre   rt   ry   r„   )r   rB   r   ©re   rp   rp   rq   Útest_issue_8666f  s   <(rá   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 )Nr„   rt   é   rŠ   )rB   re   r   r   r´   rp   rp   rp   rq   Útest_issue_7228l  s   :rã   c                   C   s0   t ttd ƒttd ƒ tƒtdƒgksJ ‚d S )Nrv   rˆ   )rB   r$   re   r+   rp   rp   rp   rq   Útest_issue_7190p  ó   0rä   c                  C   s<   t dƒ} | t| d d ƒ }| | ¡}t|| ƒg ksJ ‚d S )Nre   rt   ry   )r   r+   r   rB   )re   r|   Zf_diffrp   rp   rq   Útest_issue_21004t  s   
ræ   c                  C   st   t dƒ} ttt| t| dƒ| dkB fƒdƒƒ}|dgksJ ‚ttt| t| dƒ| dkB fƒdƒ| dd}|du s8J ‚d S )Nre   r   ry   rÛ   T)r   rB   r   r,   rM   )re   rÐ   rp   rp   rq   Útest_issue_24650{  s
   $*rç   c               	   C   s®  t dƒ\} }}}}t| d | | | d|  |d g| |gƒg ks"J ‚t| d | | | d|  | d g| |gƒg ks;J ‚t| d | d | | | d|  g| |gƒg ksTJ ‚t| d|  d d|  d|  d g| |ƒ| d|diksrJ ‚tdd||d  |d d dg|d |d d	| d |d  dgg d
¢gƒ}t|| |||ƒ| || d  | |d||| d  | iks¸J ‚t| | | | | | g| |||ƒ| | || iksÕJ ‚d S )Nzx, y, z, t, nry   rt   ru   rŠ   r‹   rl   r   rz   )r”   r   ry   r   r   )r   rB   r<   rE   )re   rf   rg   rh   rn   ÚMrp   rp   rq   Útest_linear_systemƒ  s   222<"þ*ÿ>ré   c                  C   sF   t g d¢g d¢g d¢g d¢gƒ} t| tttƒtdtdtdiks!J ‚d S )N)r   g      .@ç      $@g     à…@)ry   ry   ry   g      Y@)r   rê   g      @g      i@)g      Àr   r   r   r   g      NÀg      d@)r<   rE   re   rf   rg   )rè   rp   rp   rq   Útest_linear_system_xfail—  s   ý&rë   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   ry   )r   rB   ©r]   rp   rp   rq   Útest_linear_system_function¢  s   > ÿ&ÿrí   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 )Nrt   ry   z	x, x0, x1T©Úrealzy0_:{}zy1_:{}zc_:{}c                    s   g | ]
\}}|ˆ |  ‘qS rp   rp   )rŽ   ÚoZcoeffrà   rp   rq   Ú
<listcomp>³  ó    zMtest_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqs.<locals>.<listcomp>)r   ÚformatÚsumÚ	enumerateÚrangeÚappendr   rË   )
ZwyÚorderÚx0Úx1Zy0sZy1sr_   Úexprr’   rØ   rp   rà   rq   Ú_mk_eqsª  s   $&z9test_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqsry   râ   )rö   rB   )rü   rn   r’   r_   rp   rp   rq   Ú(test_linear_system_symbols_doesnt_hang_1¨  s
   þrý   c                  C   s0  t g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d	¢g d
¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢gƒ} tdƒ }\}}}}}}}}	}
}}}}}}}}}}i |tdƒ d “|tdƒ d “|tdƒ d “|tdƒd “|tdƒ d “|tdƒd  “|td!ƒ d “|	td"ƒ d# “|
td$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   rÅ   r  é   éL   )rˆ   é]   é"   éb   é;   é,   éC   éJ   r  é^   éG   é=   é<   é   r‹   rt   é9   râ   é   éN   )r
  é[   r  é   é@   r  rÿ   é5   éM   r  éU   é:   éW   r   r   rÈ   é$   r  r  rv   )r  éF   rl   r  éD   é+   éV   éS   éQ   r	  é   é.   r  é   r  r+  r  r   é?   r‹   )éE   r  r  é   r  r  r-  r  r  r  r,  éY   é>   r  é   é&   é   rÇ   r£   r*  )r  é   r  r  r  é-   r
  r  r  r  r  éc   éa   éR   râ   r,  r8  r  r&  é#   )r"  r5  r7  r  rˆ   r  é	   r  éZ   r:  r-  é)   r'  r*  r7  r)  r6  r  rÿ   r   )r–   r0  r%  r&  r‹   é!   r  r*  r)  rl   r(  éK   r(  r-  r   r  r2  r	  rÇ   rÿ   )rÈ   râ   rt   r	  r  é4   r  ru   é    é3   r  r$  éO   r  r+  r   r  é   r?  r  )r
  r  r3  r!  r*  r   r.  r  r
  r£   r¤   é1   r  rþ   r4  r  rv   r  r  rC  )r  r:  éP   rF  rE  r!  ry   r  rt   r  é6   r:  rE  é/   rH  r<  r;  r   r8  r  )rl   rF  r:  r  r  r  r7  r+  r7  r9  rl   r  é0   rA  rþ   rÿ   r2  rH  r9  r  )r2  r  éI   r  rA  r(  r  r4  r   r  é\   r4  r9  r%  r  r  rE  r=  r  r7  )rt   rB  r  rÿ   r  r  r+  r  ru   r>  r9  r  r  r  r  r7  r+  r  r/  r  )r  é8   ry   r  rD  r  rD  r2  r  r  r7  rI  rv   ry   rB  r  r  r;  éT   rB  )r?  rl   r#  rD  r  r<  é   r.  rÿ   r
  r,  r  r  rÇ   r  r  rN  r  r  ry   )r9  r5  r£   rA  ry   rt   r  rO  rA  r  r
  r:  r>  rK  rC  rD  r  rv   r:  r  )r  r  rA  rˆ   rˆ   r  rM  r  r:  ru   r  rJ  ry   rE  r¤   r5  r  r  r(  rA  )r4  r1  r)  r'  r  rA  r=  r   r  r   r  rÇ   r*  r  rJ  r  r  r"  rO  rv   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 ©ry   rf   )r<   r   r   rª   rB   r   )rè   Úsymsrù   rú   Úx2Úx3Úx4Úx5Úx6Úx7Úx8Úx9Úx10Zx11Zx12Zx13Zx14Zx15Zx16Zx17Zx18r®   r’   rf   rp   rp   rq   Ú(test_linear_system_symbols_doesnt_hang_2Å  s‚   í2ÿþýüûúùø	÷
öõôóòñðïír[  c               
   C   s–   t dƒ} tg d¢ddd|  dgdd| d dggƒ}t|tttgƒtd| d d	|    tdd
|  | d d	|     td|  | d d	|    iksIJ ‚d S )Nrn   )ry   rt   r   ry   ry   rv   rt   r„   r”   rŠ   r5  r£   r‹   )r   r<   rF   re   rf   rg   )rn   rè   rp   rp   rq   Útest_linear_systemLUü  s   *"þr\  c                     s  ddl m} m} tttƒd tƒtdƒgksJ ‚tt| t | ttƒd  tƒƒ| |  tdƒhks4J ‚tttƒt	 tƒt
t	ƒ dt  t
t	ƒgksLJ ‚tdttƒ t	 tƒt
t	d ƒ dt  t
t	d ƒgksjJ ‚ttttƒttƒƒtƒtd gks}J ‚ttttƒtt ƒ t	 tƒƒtt	d tt	d d ƒd  ƒtt	d tt	d d ƒd  ƒhtt	tt	d d ƒ ƒtdƒ tt	tt	d d ƒ ƒtdƒ htt	d tt	d t	d  ƒd  ƒtt	d tt	d t	d  ƒd  ƒhfv sòJ ‚tttƒd tƒtdƒgksJ ‚ttttƒdƒtƒtdƒgksJ ‚tttƒd tƒtdƒgks&J ‚ttdt ƒd tƒtddƒgks:J ‚tdtd  tƒg ksHJ ‚tddt  tƒg ksVJ ‚ttdt  tƒttdƒƒ tdƒ gksnJ ‚tdt d tdt d ƒ tƒtddƒtdttddƒƒ d ƒd  gks—J ‚tdt tdt ƒ tƒttddƒƒd gks±J ‚ttdt d	 d	ttƒ  tƒƒtd
ƒtd	ƒtt  hksÑJ ‚dtdt d ƒ d ‰ tˆ tƒ}t|ƒdkrõt‡ fdd„|D ƒƒs÷J ‚tdtdt d ƒ d tƒttddƒƒd d gksJ ‚tttƒd tƒtt gks&J ‚ddt d d  dddt d    ‰ tˆ tƒ}tdƒ }dtddƒ }tdd| d  ƒ}tdƒ}tdƒ}|t|d ƒ }	|d }
ddtdƒ  }| }|t|d ƒ }|d }||dt||	 |
  ƒ   ||dt||	|
  ƒ   ||dt|||  ƒ   ||dt|||  ƒ   ||dttdd| d  ƒ ƒ   g}||ksÒJ |ƒ‚tˆ  ¡ tƒ|ksÞJ ‚ttttƒ t	 tƒt
t	t ƒ dt  t
t	t ƒgksýJ ‚tttdt ƒ t	 tƒt
t	t ƒ d t t
t	t ƒd gks J ‚tttttƒƒ t	 tƒttt
t	t ƒƒ tt
t	t ƒdt  ƒt tt
t	t ƒdt  ƒ tt
t	t ƒƒgks[J ‚ttttƒ tƒtd ttddƒ gksrJ ‚tt	|t | t   tƒ|  t	 t	|  g| t	 |t	  gfv s•J ‚tt	|t| t ƒ  tƒ| tt	| ƒ gks®J ‚tt	|d| t    tƒ|t	 | t	  gt	| | t	   gfv sÑJ ‚tt	| t|   tƒt	|  d|  gksèJ ‚ttt t	 tƒtt	ƒttƒ gksýJ ‚tdt d tƒdtdƒtdƒ  gksJ ‚ttt	 ƒtdit	digks%J ‚ttt	 gƒtdit	digks7J ‚ttt	 d ƒtdit	digksJJ ‚ttt	 d gƒtdit	digks^J ‚ttt	 td t	d   ƒtditt	 itt	it	digks~J ‚ttt	 td t	d   gƒtditt	 itt	it	digksŸJ ‚tttdƒt ƒdt  tƒdgks´J ‚tttdƒt ƒttdƒt ƒ tƒdgksÍJ ‚tdƒ‰tt	ˆtdƒt ƒ t	ˆtdƒt ƒ  tƒdgksîJ ‚tˆtƒˆdƒ tƒdgksÿJ ‚tˆtƒˆdt ƒ tƒdgksJ ‚tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ ttdd„ ƒ ttdd„ ƒ ttttƒƒƒdtd gksUJ ‚tdddd\} }ttt| d tt| ƒd  ƒ|ƒƒd!ksuJ ‚tt	dt  t tƒtt	ƒttƒ gksŒJ ‚d S )"Nr   ©r]   r^   rv   rt   r„   r¤   ru   iíÿÿÿrâ   éüÿÿÿc                 3   ó(    | ]}ˆ   t|¡jd ddkV  qdS ©T)Zchopr   N©rË   re   rn   ©rŽ   r]   ©r   rp   rq   r“   )  ó   €& z,test_solve_transcendental.<locals>.<genexpr>ry   r‹   rÈ   r<  ia	  rÇ   rˆ   r|   c                      s   t ˆ ttƒˆ ddƒ tƒS ©Nry   rt   r   rp   ©r|   rp   rq   r™   e  rš   z+test_solve_transcendental.<locals>.<lambda>c                      s   t ˆ ttƒˆ dt dƒ tƒS ©Nrt   r   rp   rf  rp   rq   r™   f  ó    c                      s   t ˆ ttƒˆ dt ƒ tƒS ©Nry   r   rp   rf  rp   rq   r™   g  rò   c                      s   t ˆ ttƒˆ dƒ tƒS ri  r   rp   rf  rp   rq   r™   h  ó    c                   S   s0   t ttƒtttƒƒ ttƒtttƒƒ  d ƒS ©Nrv   )rB   r'   re   r&   rp   rp   rp   rq   r™   n  rå   c                   S   s   t td t t d tƒS ©Nrt   rv   r   rp   rp   rp   rq   r™   r  rš   za, bTF)rï   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^   rB   r#   re   r$   r¡   r1   rf   r-   r   r   r3   r+   r   r"   r   r   rÚ   r¨   Úexpandrg   r.   r   r[   r€   r¬   r   Ústr)r]   r^   r‘   Úresultrù   rú   rR  rS  rT  rU  rV  rW  rX  rY  rZ  rp   )r   r|   rq   Útest_solve_transcendental	  s¸    80<&þþ""þ
ú"	$"(0 (
ÿ4@
*<"(

$ü>F,&þ.F2F.*."$&(@B*2:"&""
ÿ2rs  c                  C   sŠ  t dƒ} tdƒ| ƒ}tdƒ| ƒ}tdƒ\}}}}}}t|| ||  | || ||  | g||ƒ}	|	||| ||  || ||   ||| ||  || ||   iksXJ ‚t|d |ƒdgksdJ ‚td| d |ƒtddƒgksuJ ‚t|| | ¡ || | ¡  | || | ¡ || | ¡  | g| | ¡| | ¡ƒ}	|	| | ¡|| ||  || ||   | | ¡|| ||  || ||   iksËJ ‚t| | ¡d | | ¡ƒdgksÝJ ‚td| | ¡ d | | ¡ƒtddƒgksôJ ‚d| d d| d h}
t|
||hƒ|tddƒ|diksJ ‚t dƒ}td	ƒ}|d ||ƒd  d|  d }t| |¡t||ƒ|ƒƒ| d ||ƒ gksEJ ‚t dƒ}tdƒ| ƒ}t|| || | ¡  | || || | ¡  | g|| | ¡ƒ}	|	| | ¡|| ||  || ||   ||| ||  || ||   iksšJ ‚t dƒ}td	ƒ}t||ƒ |¡||ƒ |d¡ d ||ƒ |¡||ƒ |d¡ g||ƒ |¡||ƒ |d¡ƒ}	|	||ƒ |d¡tdƒd ||ƒ |¡tdƒd iksïJ ‚t||ƒ |d¡||ƒ |d¡ d d||ƒ |d¡ ||ƒ |d¡ d||ƒ |d¡ g||ƒ |d¡||ƒ |d¡ƒ}	|	||ƒ |d¡d
||ƒ |d¡diksCJ ‚d S )Nrh   re   rf   r±   ry   rv   rt   r„   r|   r   )r   r   r   rB   r   r   r   )rh   re   rf   r¶   r·   r¸   r¹   rº   r»   ÚsolnÚeqnsr|   ÚFrp   rp   rq   Ú$test_solve_for_functions_derivatives€  sn   0  
þ",ÿÿÿ(&
ÿ$.& 4 ÿÿ
ÿ( ÿ@ÿ<6ÿÿÿ2rw  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|   rt   r„   ry   )r   re   r   rB   )r|   rv  ra   rp   rp   rq   Útest_issue_3725³  s    
Brx  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 drt   )r   rt   rŠ   r   )ry   rt   rv   r„   ry   r”   rv   rz   r   )r   r<   rB   r   r   )r]   r^   r_   r`   ÚAÚBÚCrp   rp   rq   Útest_issue_3870º  s   8:::>B<BLr}  c                  C   sJ  t dƒ} tttƒdksJ ‚tttgddksJ ‚tt| gddks#J ‚tttdt  ƒttd ftdt ffv s:J ‚tttdt  tgdtdt fksNJ ‚tdt t dƒttd ftdt ffv seJ ‚tdt t dtgƒttd fksxJ ‚tdt t dtgƒtdt fks‹J ‚ttd t dƒttd fksœJ ‚t| tƒ| tft| ffv s«J ‚tttƒd ttƒd  d t ƒtd	ttƒd  ttƒd  fksÏJ ‚tttƒd ttƒd  d t tgddksèJ ‚tttdƒƒtdfksõJ ‚tddt d  ƒd
ksJ ‚ttd tt ƒ tgdtdfksJ ‚ttd ttƒ tgdtd ttƒ dfks3J ‚ttttd  ƒ tgdtdfksHJ ‚tdt d ƒdt d dfks[J ‚tddtd   ƒtdfkslJ ‚tttƒd  tttƒd   t }t|ƒdks‡J ‚ttƒd ttƒd  }t|ƒdksœJ ‚tt	dd„ ƒ d S )NÚw©r   ry   rž   ©r   rt   rv   r   ry   rz   ©r   r   r”   c                   S   s   t ttdƒdƒS rk  )rC   r   re   rp   rp   rp   rq   r™   ç  ó    z#test_solve_linear.<locals>.<lambda>)
r   rC   re   rf   r1   r3   r   r#   r[   r¬   )r~  r   rp   rp   rq   Útest_solve_linearÍ  s6   .(.&&""ÿ2*4*&"$rƒ  c                  C   sX  t ttd  ttd   tt  dt t  t d tttgtƒtdtdtdiks+J ‚t tt ttd   dt d td t   ttgtƒtdtdiksOJ ‚t td t td  td t td   td t t  td d t t  td d  td  tttgtƒtdtdtdiksJ ‚ttt ttt  } }}t|  t|  t|  |  d|  d|  }tttf}ttf}t ||ƒtdtdtdiksÌJ ‚t |||ƒtdtdtdiksÜJ ‚t ||g|¢R Ž tdtdtdiksïJ ‚t tt t d tgƒg ksÿJ ‚t td t dt  tgƒtditdigksJ ‚t dtgƒg ks#J ‚t dtgdd	g ks0J ‚t dtgdd
g i fks?J ‚t dtgƒg ksJJ ‚tt dt  t d }tth}t ||tƒtdtdiksiJ ‚t ||tdd
ttgdhfks{J ‚t ttt ƒtdt ƒ tfƒd u sJ ‚t tt tt  dt  ttfƒtdt iksªJ ‚d S )Nrt   ry   rz   r”   rv   r„   r   Trw   r    )rt   rv   )rG   r]   re   r^   r_   rf   r3   )ÚXÚYÚZr   ÚcoeffsrQ  ZabeqrÏ   rp   rp   rq   Útest_solve_undetermined_coeffsê  sj   <ÿþÿÿ
ÿ&ÿÿ
ÿÿ
ýü,

ÿ

ÿ
ÿ ÿ$*8rˆ  c               
   C   sš  t dƒ} ttj| k | tk ƒ}t| d dkƒ|ksJ ‚t| d dkgƒ|ks'J ‚t| d dkg| ƒ|ks5J ‚t| d dkg| gƒ|ksDJ ‚t| d d dƒt| d d dƒg}t|ƒttttt	dƒ | ƒt| dƒƒttd| ƒt| t	dƒƒƒƒt
ddƒƒks~J ‚t ddd} t| d d dƒt| d d dƒg}t|ƒtttt	dƒ | ƒt| dƒƒttd| ƒt| t	dƒƒƒƒks¸J ‚t| d | d  dk | ƒttd| ƒt| dƒƒksÒJ ‚t| | d  dk| ƒttt | ƒt| dƒƒksëJ ‚tt| ƒtjkƒttd	 | k | ttd
d	ƒ k ƒksJ ‚tt
d| dk ƒƒtj| k| tk @ ksJ ‚tt
d| dk ƒƒt | k | dk @ ks1J ‚tt
| dk dƒƒtj| k| tk @ ksFJ ‚tt
| dk dƒƒt | k | dk @ ks[J ‚tt
d| ƒƒdksgJ ‚tt
d| ƒƒdgkstJ ‚tt
d| ƒƒdks€J ‚tt
d| ƒƒdgksJ ‚tt
d|  ƒƒdksšJ ‚tt
d|  ƒƒdks§J ‚ttd| ƒƒdks³J ‚ttd| ƒƒ| t k| tk @ t| dƒ@ ksËJ ‚d S )Nre   ry   rt   r   r”   Trî   rv   r‹   ru   F)r   r:   r   r³   r   rB   r   r   r;   r+   r   r3   r´   r   r   r²   r   )re   r®   Úsystemrp   rp   rq   Útest_solve_inequalities  sD   $ÿÿÿ$6ÿ428****4rŠ  c               	      sÈ  t dt ƒg ks
J ‚t tddt   ƒdgksJ ‚t tttƒ d ƒdgks(J ‚t dt  dt d  ddt   ƒg ks?J ‚t td  dt  td d  d ƒg ksVJ ‚t ttd  d d ƒg ksfJ ‚t tttd d ƒ tƒdgksxJ ‚t ttƒt tƒttƒgksˆJ ‚t ttƒƒg ks’J ‚t td t ttƒd  ttƒd  d tƒddgddgfv s³J ‚dddt d   d	 ‰ t ˆ tƒ} t| ƒdkrÕt	‡ fd
d„| D ƒƒs×J ‚t ttd ƒtd ttƒ  ttddttgttttƒttd ƒ ƒfttttƒttd ƒ ƒ fhfksJ ‚t td t
d  t
d td   ƒtt ittit
digks0J ‚t td ddtd    ƒg ksCJ ‚t ttt
  t tƒdgksTJ ‚ttdd„ ƒ ttdd„ ƒ d S )Nry   ru   rt   rv   rz   r   r”   r„   rÈ   c                 3   r_  r`  ra  rb  rc  rp   rq   r“   F  rd  z"test_issue_4793.<locals>.<genexpr>Tr    c                   S   s   t ttƒttƒ tƒS rŒ   )rB   r$   re   r#   rp   rp   rp   rq   r™   M  ó    z!test_issue_4793.<locals>.<lambda>c                   S   s   t dt ttƒ d ƒS rl  )rB   re   r#   rp   rp   rp   rq   r™   N  rj  )rB   re   r+   r#   rf   r$   r3   r1   rÚ   r¨   rg   r[   r€   ©r‘   rp   rc  rq   Útest_issue_47939  s,   .. $ B
&&8þB&"r  c                  C   s8  t ttƒƒt ttd ƒƒ  krdgksJ ‚ J ‚t ttd ƒƒdgks&J ‚tdƒ} t d|  ttƒ tƒg ks9J ‚t dt td  d tƒdgksKJ ‚tt td dt   t¡ƒƒtjtdƒhkscJ ‚td	ƒ}t dd
t |tƒ  |tƒ |tƒƒtt	d
dƒ gks„J ‚t dt
d
t d
ƒ d tƒt	ddƒgksšJ ‚t ttƒtttƒƒ d ƒt	ddƒtdƒd  d gks¸J ‚tt ttttƒƒttt ƒƒ d ƒƒƒttdƒ d d ƒttdƒd d ƒhdttdƒ d ƒ dttdƒd ƒ htdtdƒ d ƒtdtdƒ d ƒhfv sJ ‚tt tttƒtt ƒ d ƒƒƒttdƒ d ƒttdƒd ƒhks2J ‚tt tt tdt   d tƒƒt	ddƒtd
ƒd  dt  t	ddƒtd
ƒd  dt  hksdJ ‚t ttt ƒtt t ƒ d tƒtt tdƒ gks‚J ‚t tt tt  d tƒtdƒttƒttƒ  gtdƒttt ƒ gfv sªJ ‚tj}t tdt ƒtdƒ tƒdt|t	ddƒtdƒt d   ƒt|t	ddƒtdƒt d   ƒgdt| d tdƒ| t d  ƒt| d tdƒ| t d  ƒgfv sJ ‚tddd}t d| d |d  ƒg ksJ ‚d S )Nrv   r   ry   r]   rŠ   rt   rÈ   rO  r|   ru   r<  i´~ûÿi©æ  r„   r”   r-  r^  rd   T©Úpositive)rB   r+   re   r   r¡   r   r   r³   r   r   r*   r>   r#   r$   rf   rg   ÚExp1r   )r]   r|   r   rd   rp   rp   rq   Útest_PR1964Q  sF   2$0:,<(((&ý
ÿ  
ÿ :
ÿ<ÿ.
ÿDDþ&r‘  c                  C   sŒ  t ddd} t| d d | ƒg ksJ ‚t dddd}t|d |d  d| d  |ƒdgks0J ‚t ddd} t d	ƒ}t| d
|  d d|  d|  d g| |ƒg ksTJ ‚t| | d|d  g| |ƒtdƒtdƒ fgksnJ ‚t d	dd}t| d |d t| ƒ  || dd|| t| d ƒ igks“J ‚tddd\} }}t|d | d  |d |d  t| ƒ  || |dd|| t| d ƒ igksÄJ ‚d S )Nre   Trî   rt   ry   rn   )Úintegerr  rŽ  rf   ru   rŠ   r‹   rl   rw   zx y z)r   rB   r+   r#   r   )re   rn   rf   rg   rp   rp   rq   Útest_issue_5197~  s   ,44>Tr“  c                   C   s¸   t ttttt   tddƒttƒtjttƒ hksJ ‚t ttttt   tddƒttƒttƒ hks6J ‚tddt d  dtd  d fƒg ksLJ ‚tddt d  ƒg ksZJ ‚d S )NFrÆ   Try   rt   rv   )r¡   rB   re   rf   r+   r   r³   rp   rp   rp   rq   Útest_checking  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 )Nrt   ry   ru   rl   zC1 C2r|   r]   r„   rŠ   r”   rv   rz   )rB   r+   re   r#   rf   r$   r   r   r   r   r   r   r  r3   r1   r'   r&   r¡   r/   r4   )ZC1ZC2r|   r]   r   rp   rp   rq   Útest_issue_4671_4463_4467š  s>   &
ÿ(>
ÿJ$$
þ  
þ$$þ@6(&&ÿ
ÿ$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,trt   r”   ry   rv   r„   Tr    rˆ   )r   r¡   rB   re   rf   r4   r+   r1   r#   r3   r$   r   r   rg   r²   )rÐ   rh   r’   rp   rp   rq   Útest_issue_5132·  sr   02ÿ.þÿ$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?rt   ry   T)ÚmanualZminimal©r   rf   re   rÚ   rB   ©ZlamZa0Zconcr]   r^   r’   Úsymrp   rp   rq   Útest_issue_5335ã  s   ."
þ
rž  ZHangsc                  C   sœ   t dƒ\} }}d}d}| dt  |dtd   t  |t d t  |dtd   t dt  |t  tt | g}tt|g}tt||ddƒdksLJ ‚d S )Nr—  r˜  r™  rt   ry   F©Zrationalr›  rœ  rp   rp   rq   Ú_test_issue_5335_floatð  s   ."
þ
r   c                   C   sH   t ttd t d gtgƒƒtt d ƒ ftt d ƒfhks"J ‚d S )Nrt   r„   )r¡   rB   re   rf   r+   rp   rp   rp   rq   Útest_issue_5767ý  s    ÿr¡  c                  C   s  t dddd\} }}}}}t dddd\}}}t dddd}	dtdƒd  ttdƒd   | tdƒd	 td |	d    d
|tdƒd   |	tdƒd    dtdƒd  ttdƒd   | d|tdƒd   |	tdƒd     }
dtdƒ t d }|
||	fS )NzD, R, H, B_g, V, D_cT)rï   r  zSigma_f, Sigma_a, nure   rt   rv   iÁ‡ i'  r‹   ry   râ   rÈ   éd   iá  )r   r   r   r+   )ÚDrk   ÚHZB_gÚVZD_cZSigma_fZSigma_aÚnure   r   Úexpectedrp   rp   rq   Ú_make_example_24609  s   >"ÿFþÿ
r¨  c                  C   sP   t ƒ \} }}t| |dd|gksJ ‚t|  ¡ |ƒ\}t|| ¡  ƒdk s&J ‚d S )NT©r¢   g›+¡†›„=)r¨  rB   rn   Úabs)r   r§  re   Z	solapproxrp   rp   rq   Útest_issue_24609  s   r«  c                  C   s(   t ƒ \} }}tt| |ƒƒ|gksJ ‚d S rŒ   )r¨  rÚ   rB   )r   r§  re   rp   rp   rq   Útest_issue_24609_xfail  s   r¬  c                   C   sê   t ttd dt  d tt d gttgƒƒtjtdƒfdtdƒ dtdƒ fdtdƒ dtdƒ fhks7J ‚ttd t d td t gƒg ksKJ ‚ttd t d tt d gttfƒttd t d tt d gttfƒkssJ ‚d S )Nrt   rv   ry   ru   r„   )r¡   rB   re   rf   r   r²   r+   rp   rp   rp   rq   Útest_polysys,  s   ,"ÿÿ(,ÿÿ
ÿÿr­  c            	   
      s´  t tdd„ ƒ t tdd„ ƒ tdtd‰‡fdd„} ‡fdd	„‰td
ƒd u s(J ‚| tttƒƒtg fƒs5J ‚| tttƒd
 ƒtd
 g fƒsFJ ‚| tttƒttdƒ d ƒˆd ˆd  d ˆˆd t gfƒshJ ‚| tttƒttdƒ d ƒtd d g fƒs€J ‚| tttƒtd
 td
dƒ  ƒtd td
 d  g fƒsžJ ‚| tttƒttd
 ƒ tdt ƒ ƒdtdƒ t dt  d
 g fƒsÃJ ‚| tttƒttd
 ƒ d ƒdt d g fƒsÜJ ‚| tttƒttd
 ƒ td
t ƒ ƒdtd  dt  g fƒsýJ ‚| tt	ttƒ t
ttƒ  tttƒ  tttƒ  ƒt	ttƒ t
ttƒ  d tttƒ tttƒ  d  g fƒs9J ‚| tttƒtd
t ƒ ƒdt d
 g fƒsQJ ‚| tttƒtd
t ƒ d ƒtd t d g fƒsmJ ‚| tttƒtd
t ƒ tdt ƒ ƒdtd  dt  d
 g fƒs‘J ‚tttƒtd
t ƒ tdt ƒ d ƒdtd  dtd   dtd   dt  d g fdtd  dtd   dtd   dtd   d g ffv sÞJ ‚tttƒtd
t ƒ tdt ƒ td
dt  ƒ ƒdtd  dtd   d td   d!t  d g fksJ ‚| tttƒttd
 ƒ ƒtjg fƒs*J ‚ttƒttd
 ƒ td
ttƒ ƒ }| t|ƒdtd  dt  g fƒsPJ ‚tt|d"d#ƒtjtddƒhkscJ ‚t|ƒg kslJ ‚ttttƒttd
 ƒ td
ttƒ ƒ ƒƒtjtddƒhksJ ‚| tttƒttd
 dƒ dttƒ  tƒtd$ƒg fƒs«J ‚| tttd
t  ƒtd
 td
dƒ  ƒtd td  td  dtd   t d
 g fƒsÚJ ‚| tttd
t  ƒdttƒ  tƒdt t t dt  g fƒsýJ ‚| tttƒtd
t ƒ d tƒtd t d g fƒsJ ‚tttttd ƒƒƒdgks+J ‚tttttd ƒ dƒƒdgks>J ‚ttd
ttdt d ƒ ƒƒg ksRJ ‚ttttdt d ƒd tƒƒƒtj tdƒhksnJ ‚ttttdt d
 ƒttd ƒ dƒƒƒtdƒtd%ƒhksŽJ ‚ttttd& ƒd tdt ƒƒƒd'gks¥J ‚tdt d td
dƒ d ƒdgksºJ ‚tttd
 ttd dtd   t dƒ ƒƒtd(dƒtd(dƒhksÞJ ‚tttdtd  d& ƒdt  ƒƒtdƒ tdƒhksüJ ‚ttdt d ƒttd
 ƒ ttd ƒ ƒd)gksJ ‚tttd ƒtdt d
 ƒ dttd
 ƒ  ƒdgks6J ‚tttƒttd& ƒ d* ƒdgksJJ ‚tttd ƒttƒ d ƒdgks^J ‚ttdtd  d ƒdt d  ƒd)gksvJ ‚tttƒd d ƒd+gks†J ‚tttd ƒttƒ d ƒg ks™J ‚tttd
 ƒt d& ƒd,gks«J ‚tttd ƒd ƒd-gks»J ‚ttd.t ttd d ƒ ƒd& ƒdgksÓJ ‚tttƒttd
 ƒ tttƒƒ ƒg ksêJ ‚tdt d
 ƒttƒ tdd
t  ƒ }t|ƒd) }t|ƒg ksJ ‚t|ƒg ksJ ‚t|dt  ƒtd(d/ƒgks'J ‚t|dt  ƒg ks4J ‚tttd
 dƒttdƒ ƒtd td  dtd   dt  d
  g fks\J ‚| ttttdƒ ttdƒd  ttƒ tƒˆd ˆd  ˆ ttƒ ˆˆd t gfƒs‹J ‚| tttƒttdƒ t ƒˆd ˆd  t ˆˆd t gfƒs®J ‚tttƒttdƒ d ƒd
gksÁJ ‚t td0d„ ƒ t td1d„ ƒ tttttdƒ ƒttt dƒ tƒtttd
dƒ t tddƒ  gksöJ ‚| tttƒttd
 dƒttd ƒ  d ƒˆd, dˆd   d2ˆd   d*ˆd   d3ˆd   d!ˆd   d4ˆd   d5ˆ  d6 ˆˆd t gfƒsEJ ‚ttd
 dƒttdƒ }t|ƒdt d
 g fks`J ‚ttƒttd
 ƒ td
t ƒ dtdƒ d  }| t|ƒd7td  d8td   d9td   d:t  d; g fƒsšJ ‚| tttdƒttdƒd  d
 ƒˆd ˆ d
 ˆˆd t gfƒs¾J ‚| tttdƒttdƒd  d
 ƒtd dtd   t d
 g fƒsâJ ‚ttd< ƒd u síJ ‚| ttttt dƒ ttt dƒd  ƒˆd ˆ t ˆˆd t t gfƒsJ ‚| ttttt dƒ ttt dƒd  tƒˆd ˆ t ˆˆd t t gfƒsBJ ‚| ttttt dƒ ttt dƒd  tƒˆd ˆd  ˆ t ˆˆd t t gfƒsqJ ‚| tttd
 dƒttd
 dƒ tddƒ ƒˆd ddtd
dƒ  ˆd   ˆd  d,dtddƒ  ˆd   d,dtddƒ  ˆd   ddtddƒ  ˆ  d ˆˆd t d
 gfƒsÐJ ‚t td=d„ ƒ tttdƒttdƒ d ƒd
gksëJ ‚ttƒttd
 ƒ td
t ƒ dtdƒ d  }| t|ƒdt d d>td  d?td   d@t  dA  g fƒs%J ‚tdBƒ‰ t|ƒˆ ks2J ‚| tttttd
 dƒ ƒttd
 dƒ d ƒˆd ˆd  dˆ  d ˆˆd t d
 gfƒsdJ ‚ttd d
 dƒttd d
 dƒ d }| t|ƒˆd d,ˆd   dCˆd   dDˆd   dDˆ  dE ˆˆd td  d
 gfƒs¨J ‚ttttd
 dƒ ƒttd
 dƒ d }| t|ƒˆd dˆd   d&ˆd   dˆd   dFˆd   dˆ  d ˆˆd t d
 gfƒsðJ ‚| t|dGdHˆd dIˆd   dJˆd   dKˆd   dLˆd   dMˆ  dN ˆˆd t ttd
 ƒ gfƒ	s*J ‚| ttttttdƒd
 ƒ ƒttdƒ d ƒˆd* dˆd   dˆd&   dˆd   ˆd  dˆd   dOˆd   dPˆ  d. ˆˆd t gfƒ	sxJ ‚ttttƒdƒt ttd
 dƒ d
 ƒtdQ td ttƒd   dtd  ttƒd   dt ttƒd   ttƒd   g fk	s¼J ‚ttdRƒƒd u 	sÇJ ‚| ttdRƒtƒˆdt  ˆ d
 ˆˆd t t gfƒ	sæJ ‚tttjt  t tƒtd
t  td  g fk
sJ ‚ttttƒt td  d
 tƒƒdk
sJ ‚ttdStd  dTtd td
dƒ  td   dUtd tddƒ  t  dt  dV td"dWƒdk
sKJ ‚tdXƒ}t|tƒdtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd  td
ƒ d tdƒt d    dtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd  td
ƒ d tdƒt d    dtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd   gks
J ‚ttd
 dƒttdƒttdƒ  }| t|ƒdˆd%  dˆd/   ˆd  d
 ˆˆdQ t gfƒs=J ‚| t|d ƒdˆd%  dˆd/   dˆd,   ˆd  d*ˆd   dˆd   d*ˆd   d*ˆd   d& ˆˆdQ t gfƒsJ ‚| tttdƒttd
 dƒd  ttd dƒ ƒˆd\ˆd  d]ˆd   d^ˆd&   ˆd  d_  ˆˆd t d
 gfƒs¾J ‚| tttdƒttd
 dƒ ttd dƒd  ƒd[ˆd%  d`ˆd*   dTˆd/   dZˆd,   daˆd   dbˆd   d_ˆd&   dcˆd   ddˆd   deˆ  ˆˆd t d
 gfƒsJ ‚| tttdƒd ttd
 dƒ ttd dƒ ƒdeˆd%  ddˆd*   d_ˆd/   dZˆd,   dcˆd   dbˆd   dTˆd&   daˆd   d`ˆd   d[ˆ  ˆˆd t d
 gfƒs|J ‚| tttdƒd ttd
 dƒ ttd dƒ d ƒdeˆd%  dfˆd*   dgˆd,   dhˆd   diˆd   djˆd&   dkˆd   dlˆd   dmˆd   dnˆd   doˆd   dpˆ  dq ˆˆd t d
 gfƒsëJ ‚tttƒttd
 ƒ td
t ƒ tdt ƒ ƒ‰ tˆ ƒd
krtˆ d) ƒd d… drksJ ‚tdsƒ}|dt dt  ttd td  ƒ  }|tdd&ƒ tdƒ| dI  ‰ t|td"d#}t|ƒD ]"}ttt  t|¡ t¡td"d"dt}t‡ fdudv„|D ƒƒrl nqKJ ‚tttd
 ƒttdƒ d ƒtdwƒks†J ‚ttttd
 ƒƒttd
dƒ  d ƒtdxƒks J ‚tttƒtttƒd
 dƒ d ƒtdyƒks¸J ‚tdzƒ}| t|ƒˆˆd  tdƒˆd  t  d{dtddƒ  dtd
dƒ  ˆd   d|d*td
dƒ  ˆd   d}dtddƒ  dtddƒ  ˆd  t  d~ˆd   d~tdƒ ˆd  t  dd€td
dƒ  ˆd   d dtdƒ t    ˆˆd d‚t  tdƒtdƒtd  d„t  d… ƒ  d† gfƒsTJ ‚t|ƒg ks]J ‚ttdƒttdƒ ttdƒ }| t|ƒˆdQ dˆd%   dˆd/   ˆd  t ˆˆdQ t gfƒs’J ‚ttdƒttdƒ ttt dƒ }| t|ƒˆt ˆd*  dˆd/  t  dˆd,  td   ˆd td   dˆd  td   dYˆd&  td   dˆd  td   dˆd  td   dˆd  td   td   ˆˆd tt  gfƒsJ ‚t td‡d„ ƒ tttd
ƒd   ttd
ƒd   dtd
ƒd   d(tdƒd  dtd
ƒd    ƒ}| t|ƒˆd  ˆd  dtd
ƒd   d(tdƒd  dtd
ƒd    ˆˆdQ t gfƒsqJ ‚ttƒd
 ‰tˆd ˆd  ƒtd dtd   dt  d g fks–J ‚tttd
  d d tƒd u s¨J ‚ttt ƒt tttt ƒ ƒ t tttt ƒ ƒ }t|tƒtd
 gksÏJ ‚t|ƒd u sØJ ‚d S )ˆNc                   S   s,   t ttƒttd ƒ tdttƒ ƒ d ƒS ©Nry   rv   )rL   r+   re   rp   rp   rp   rq   r™   8  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 )Nry   rv   rt   )rL   r+   re   r   rf   rp   rp   rp   rq   r™   :  ó   *rÏ   )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 ©Nry   r   )Úboolrp  )Úrvr‘   ra   r]   )Ús_checkrp   rq   r§   A  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   ry   )rª   Úatomsr   ÚziprÚ   rË   rp  rq  )r³  r‘   r`   Úreps©rÏ   rp   rq   r´  I  s   66&ÿztest_unrad1.<locals>.s_checkry   rv   rt   r‹   ru   r  rz   r¤   r<  r„   r+  ix  iè  ià  i  râ   iÜ  iæ	  i¼  é©   r>  r  éè   é    FrÆ   z32*sqrt(x)*(x + 1)**(1/3) + x - 4*y + (x + 1)**(2/3)r  rÈ   iúÿÿÿr”   r   r£   rF  rˆ   rÀ   r-  r  c                   S   s(   t ttƒttdƒ ttd dƒ d ƒS )Nrv   ry   ru   rt   )rB   r+   re   r*   rp   rp   rp   rq   r™   ±  s   (c                   S   s   t tdƒ ttƒt  ƒS rg  )rB   r+   r&   re   rp   rp   rp   rq   r™   ´  rš   rÿ   r6  éÔ   éÀ   rM  i	=  iÈ£ im i { i  rn  c                   S   s6   t ttdƒttdƒ ttdƒ  ttd t d ¡ƒS )Nrt   rv   r„   ru   ry   )rL   r*   re   rË   rp   rp   rp   rq   r™   Î  s   6i5  iì  iÀ‰ i D z¥
        [4/5, -1484/375 + 172564/(140625*(114*sqrt(12657)/78125 +
        12459439/52734375)**(1/3)) +
        4*(114*sqrt(12657)/78125 + 12459439/52734375)**(1/3)]r   rG  r3  rE  T)Z_reverserO  rK  é»   é  éä   r1  r  rB  rl   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 - 1r0  i   iW  i   iÀ  rJ  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0.73rv  ©r¢   r§   c                 3   s    | ]
}|ˆ    ¡ jV  qd S rŒ   )rp  Úis_zerorb  rŒ  rp   rq   r“   3  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™   rC  éf   iT  i06  r5  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 )Nrv   ru   )rL   r*   re   rf   rp   rp   rp   rq   r™   Y  s   & )!r[   r€   r   r   rL   r+   re   r*   r   r]   r^   r_   rf   r`   r   r²   r¡   rB   r³   r   rN   r   rh   r&   r´   rÚ   rr   r   ÚreversedrË   r   Úanyr#   )	r§   r   rg   rd   ra   rv  r„  Úxir…  rp   )r‘   rÏ   r´  rq   Útest_unrad16  s0  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&$ÿ*Nÿÿÿ
ÿ02
ÿ 
ÿ 
ÿ("
ÿ*"
ÿ**
ÿ*Bÿÿÿÿ
ÿ(02
ÿ,.
ÿ(6ÿ
ÿ(Bÿ
ÿBÿ
ÿ,Jÿÿÿ
ÿ&F
ÿþ	&
ÿ6,,ÿÿÿÿ
ÿH
ÿ
ÿÿÿ
ÿÿÿ

ÿ
ÿÿÿÿ
ÿÿÿ"ÿü"2
ÿN
ÿÿÿ
ÿ.2ÿ
ÿ.:
ÿ
ÿ
ÿ
ÿÿÿÿ
ÿ.:
ÿ
ÿ
ÿ
ÿÿÿÿ
ÿ2:
ÿ
ÿ
ÿ
ÿ
ÿ
þþþþ
ÿ
ÿ
ÿ,("ÿ,40Fÿ*ÿ
ÿþþþý"ÿÿÿý
ÿ:
ÿ"Bÿÿÿÿþþþ
ÿÿVP
ÿ>$4rÏ  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 )Nry   r„   rt   )r+   re   rB   r   r´   rc  rp   rp   rq   Útest_unrad_slowl  s   DrÐ  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 )
Nrv   rt   ry   ru   r”   r„   râ   rˆ   r   )rB   r*   re   r   rW   rp   rp   rp   rq   Útest_unrad_failt  s   6&BÿrÑ  c                     s  t dƒ\‰ } }}|ˆ d  | d  }| t|ƒ tt|ƒd d ƒ ˆ t|ƒ t|ƒ tt|ƒd d ƒ i}t||ƒdks?J ‚ttˆ dƒˆ diƒdu sMJ ‚ttˆ dƒˆ diƒdu s[J ‚ttˆ dk dƒˆ diƒdu skJ ‚ttˆ dk dƒˆ diƒdu s{J ‚ttˆ dk dƒˆ diƒdu s‹J ‚ttˆ dk dƒˆ diƒdu s›J ‚ttˆ d ˆ d d ƒˆ diƒdu s¯J ‚tˆ d ˆ d d gˆ dƒdu sÁJ ‚tˆ d ˆ d d gˆ dƒdu sÓJ ‚ttˆ d d ƒˆ dƒdu sãJ ‚tdi ƒdu sìJ ‚tdˆ d gˆ dƒdu súJ ‚tddˆ gˆ dƒdu sJ ‚t| ˆ dƒdu sJ ‚tˆ d ˆ ddd	du s"J ‚tˆ d ˆ ddd	du s1J ‚ttd
ˆ  ƒˆ ttdƒd ƒiƒdu sGJ ‚ttd
ˆ  ƒˆ ttdƒd ƒt	t
  iƒdu saJ ‚tdˆ d  ˆ dƒdu spJ ‚tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nz
x, y, r, trt   ry   TFr   g»½×Ùß|Û=rn  ©Z	numericalrL  ru   iè  c                      s
   t ˆ dƒS ri  ©rM   rp   rà   rp   rq   r™   –  s   
 ztest_checksol.<locals>.<lambda>c                      s   t g ˆ dƒS ri  rÓ  rp   rà   rp   rq   r™   —  r   )r   r+   r4   rM   r   r   r>   r#   r$   r   r   r[   r¬   )rf   rÐ   rh   r   Zdict_var_solnrp   rà   rq   Útest_checksol}  s6   &ÿ    ($$ ,4rÔ  c                   C   s¢   t td ƒdtfksJ ‚t dƒdksJ ‚t tdt ƒd tƒdtdƒ tfks)J ‚t tdt tt  ƒd tƒtd tdƒ tfksDJ ‚t ttƒtdfksOJ ‚d S )Nrt   )rt   r   ry   rv   r   )rK   re   r#   r$   r]   rp   rp   rp   rq   Útest__invertš  s
   *6rÕ  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 )Nrt   rv   r„   )rB   r]   re   r$   r#   r"   rp   rp   rp   rq   Útest_issue_4463¢  s   2&2rÖ  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:rry   TF)rš  r§   r¢   )r   rÚ   rB   )r]   r^   r_   r`   ra   r|   r}   rc   rØ   Újrb   Úlrj   rn   rð   rd   ri   rÐ   rQ  r’   rp   rp   rq   Útest_issue_5114_solvers¨  s   ,****û"rÙ  c                     s  t dƒ\} }}}}}t dƒ\}}}}	}
}| | | || | || | |  | | d|  d|  d|  d|  |d  d | |	 | | d| d|  d|  |
 |d|  d|  | f	}| || |d| d|  d	|  d
|  d ||| |	|| || d d| d  |d  |||
d| d|  d|  ig‰ | ||
|||||	f‰t|gˆ¢R ddddœŽˆ ks¹J ‚t|gˆ¢R dddœŽ‡fdd„ˆ D ƒksÐJ ‚t|gˆ¢R ddiŽg ksßJ ‚t|gˆ¢R Ž g ksëJ ‚‡ fdd„|D ƒdd|| | | dddddg	ksJ ‚d S )NúI1:7údI1,dI4,dQ2,dQ4,Q2,Q4rz   rt   rv   r£   r^  râ   r„   r‹   rÿ   TF)rš  r§   rx   ©rš  r§   c                    s"   g | ]‰ t ‡ fd d„ˆD ƒƒ‘qS )c                    s   g | ]}ˆ   ||¡‘qS rp   )Úgetr×   rì   rp   rq   rñ   Ù  rj  z.test_issue_5849.<locals>.<listcomp>.<listcomp>©r©   )rŽ   )Úvrì   rq   rñ   Ø  s    ÿz#test_issue_5849.<locals>.<listcomp>rš  c                    s   g | ]	}|  ˆ d  ¡‘qS ©r   )rË   )rŽ   ÚeirŒ  rp   rq   rñ   ß  s
    ÿÿr   ©r   rB   ©ZI1ZI2ZI3ZI4ZI5ZI6ZdI1ZdI4ZdQ2ZdQ4ZQ2ZQ4ra   rp   )r‘   rß  rq   Útest_issue_5849¸  s@   


*÷$ù	" ÿ
ÿÿrä  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.
    rÚ  rÛ  rz   rt   rv   r£   Nrâ  rã  rp   rp   rq   Útest_issue_5849_matrixã  s   



*÷$rå  c                  C   s®  t dƒ \} }}}}}}}| |  | d| d  d| d  d| d  d|  d  | | d| d  |d  | | |d  | d| d	 d| d	  d|  d	  | | |d  d
| d  |  | | | |d	  | d  d| d |d  |  d| d d|  d|  d  | g	}| d|d|d|d|d|di| d|| |d|tdƒd |d|di| d| |d|||d|tdƒd	 |dig}	t||dd}
|
|	ksÕJ |
|	fƒ‚d S )Nza, b, c, d, f, g, kru   r‹   rt   r<  r„   rv   r  r5  rÇ   r   rz   Trw   )r   r   rB   )r]   r^   r_   r`   r|   r}   rb   ZunknownsZ	equationsZanswerÚgotrp   rp   rq   Útest_issue_21882þ  s"   <" ÷$&ýrç  c                     sŽ  t tdƒ\‰ } }tdƒ}tˆ tƒtƒ}t| |ƒ|ƒ}tˆ tƒˆ tƒ t¡ ˆ tƒƒ| gks0J ‚tˆ tƒd ˆ tƒƒdgks@J ‚tˆ tƒdˆ tƒ t¡  ˆ tƒƒd| gksYJ ‚tˆ tƒdˆ tƒ t¡  gˆ tƒƒˆ tƒd| iksvJ ‚tˆ tƒdˆ tƒ t¡  ˆ tƒd t d gˆ tƒtƒd| d|d  d fgks¢J ‚tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒdd||ƒ| |ƒgtˆ |ƒd | |ƒd  | ƒ ˆ |ƒ | |ƒftˆ |ƒd | |ƒd  | ƒˆ |ƒ | |ƒfhfks2J tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒddƒ‚ˆ tƒ td¡ˆ tƒ| tƒ  d| tƒd  gˆ tƒ| tƒg}t|d	diŽd
 tdƒ tdƒftdƒtdƒ fhksoJ ‚ˆ tƒd | tƒ dˆ tƒ t¡  | tƒd d g}t|ˆ tƒ| tƒddˆ tƒ| tƒgtd| d ƒ t	dƒftd| d ƒt	dƒftd| d ƒ t	dƒ ftd| d ƒt	dƒ fhfksÓJ ‚t
t‡ fdd„ƒ tˆ tƒˆ tƒ t¡ tgdˆ tƒtˆ tƒtƒ d
fksüJ ‚tˆ tƒttttfƒ tgdˆ tƒttttfƒ d
fksJ ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ d
fks@J ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ fkscJ ‚ttˆ tƒ|  ˆ tƒd
 |  tgdtd
| fksJ ‚tttdt tƒ ƒtdfks“J ‚tttttƒ tgdtdfks¦J ‚tttttƒ d tgdtdtd
  fks¿J ‚tttttƒd  ttƒƒƒtt ƒ tt ƒhksÜJ ‚ttttƒ tddttƒ gksðJ ‚tttƒttƒ tddg ksJ ‚ttttƒ tddttƒgksJ ‚ttd t d tddtd  d gks-J ‚ttd t d td ddt d gksEJ ‚d S )NZfghr]   rv   rt   r„   r<  Tr    r¡   ry   c                      s$   t ˆ tƒˆ tƒ t¡ ˆ tƒgdS )Nr€  )rC   re   r   rp   rf  rp   rq   r™   =  r¥   z!test_issue_5901.<locals>.<lambda>r€  rz   r   r•   )r{   r   r   r   re   rB   r   rf   r+   r   r[   r¬   rC   r9   r¡   r#   r1   r3   )r}   rc   r]   r£  ÚGr¯   r’   rp   rf  rq   Útest_issue_5901  s®   ÿÿ"ÿ$ÿ8ÿ@ÿ0.þþ@ÿü>"
ÿ6ü
ÿÿ
ÿ
ÿ"
ÿ"
ÿ(

ÿ
ÿ
ÿ
ÿ
ÿ

ÿ$
ÿ
ÿ
ÿré  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 )Nrt   çš™™™™™¹?TrŸ  r;  rˆ   Fc                 s   ó    | ]}|j V  qd S rŒ   ©Z	is_Numberrb  rp   rp   rq   r“   `  ó   € z"test_issue_5912.<locals>.<genexpr>c                 s   rë  rŒ   rì  rb  rp   rp   rq   r“   b  rí  )r¡   rB   re   r   r´   r+   rÚ   r¨   rŒ  rp   rp   rq   Útest_issue_5912\  s   $ÿ"&rî  c                  C   s†  dd„ } t td ddd jsJ ‚t td ddd jsJ ‚t ttj ddd js,J ‚t td d dd js9J ‚t ttj d dd jsGJ ‚| tdd	t  ƒd
dt  ƒsXJ ‚ttt	fD ]"}t|dd	t  gƒƒ}t
|ƒ|u r}| t|ƒd d
dt  ƒsJ ‚q]ttd	t dd	t  giƒ ¡ ƒd \}}| |d	t ƒr§| |d d
dt  ƒs©J ‚| ttd	t ƒƒtdt ƒƒsºJ ‚| tdtd	  ƒdtd	  ƒsËJ ‚| tdtd	  dddtd  ƒsÞJ ‚| ttd	t ƒƒtdt ƒƒsïJ ‚| ttd ƒtd ƒsüJ ‚| ttd d	t  ttddƒƒ d ƒtd dt  d ƒsJ ‚dt t t }t dt | d dt | d t| d fƒg ksAJ ‚d S )Nc                 S   s   t |  t¡ƒt | t¡ƒkS rŒ   )rÚ   rµ  r   ©Úe1Úe2rp   rp   rq   Útestf  s   z!test_float_handling.<locals>.testrn  TrŸ  r   Fry   rt   ç      ð?g       @rv   g      @rÉ   r„   g!ÌÈ,‹ÿ?r¢  gffffffæ?g333333ã?gš™™™™™É?g333333Ó?rê  )rB   re   Zis_RationalZis_Floatr   r´   rD   rª   r©   r¡   ÚtypeÚitemsr1   r#   r   r_   rg   rh   )rò  Zcontainr‘   rb   rß  Ztotrp   rp   rq   Útest_float_handlinge  s,   ",*(""&"&
ÿ<rö  c                  C   s*   t ddd} t| d d ƒdgksJ ‚d S )Nre   TrŽ  rt   ry   râ  rà   rp   rp   rq   Útest_check_assumptions  ó   r÷  c                   C   sì   t ttd ƒttd ƒ d ƒg ksJ ‚t ttd ƒttd ƒ d ƒtt tddƒ t t d tt d tt tddƒ gksCJ ‚t ttd ƒttd ƒ d d ƒtt tddƒ t t d tt d tt tddƒ gkstJ ‚d S )Nrv   ry   rŠ   r„   rt   )rB   r(   re   r   r   r   rp   rp   rp   rq   Útest_issue_6056„  s   (8ÿ"8ÿrù  c                  C   sV   t  ttttt ƒƒƒttt ƒƒ ƒ } t| t dƒdu sJ ‚t| t dddd u s)J ‚d S )Nrt   TFrÒ  )re   r#   r"   r$   rM   rc  rp   rp   rq   Útest_issue_5673Œ  s   &rú  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$R, C, Ri, Vout, V1, Vminus, Vplus, sÚRfTrŽ  rz   ry   r”   rž   rt   rv   r   ru   r‹   ©r   rB   r+   )
rk   r|  ZRiZVoutZV1ZVminusZVplusrÏ   rû  r’   rp   rp   rq   Útest_exclude’  sL   ÿ"(ý$(üü
ú,@ü,@üû$ üörý  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 )Nru   r„   rv   rt   rÈ   ZZZ)Údomain)re   r   r¡   rB   r>   Z	all_rootsr¸  rp   rp   rq   Útest_high_order_rootsº  s   *,rÿ  c                     sÐ  dddœ} dddœ}t tt d dt t d gfi | ¤Žtdtdiks&J ‚t tt d dt t d gfi |¤ŽtdtdiksBJ ‚dd	„ }|t tt t tt t t gfi | ¤Žƒdks`J ‚|t tt t tt t t gfi |¤ŽƒdkszJ ‚|t tt t tt t gfi | ¤Žƒdks’J ‚|t tt t tt t gfi |¤ŽƒdksªJ ‚tg d
¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢gƒ}ttdddƒ}tdgdgdgdgdgdgdgdgdgdgdgdggƒ}|| | }t |ƒg ksJ ‚t |ddg ksJ ‚tdd„ t tt t tt t gƒ 	¡ D ƒƒs*J ‚dD ]2‰ tdd„ t tt t tt t gˆ dd 	¡ D ƒƒrKJ ‚t
t‡ fdd „ƒ t
t‡ fd!d „ƒ q,t
td"d „ ƒ d S )#NT©ÚquickÚ
particularFru   rt   ry   rv   c                 S   s   t dd„ |  ¡ D ƒƒS )Nc                 S   s   g | ]}|d kr|‘qS rà  rp   )rŽ   re   rp   rp   rq   rñ   Å  rj  z>test_minsolve_linear_system.<locals>.count.<locals>.<listcomp>)rÚ   Úvalues)Zdicrp   rp   rq   ÚcountÄ  r¿   z*test_minsolve_linear_system.<locals>.count)ry   ry   ry   r   ry   ry   r   ry   r   r   ry   ry   ry   r   )ry   ry   r   ry   ry   r   ry   r   ry   r   r”   r”   r   r   )r”   r”   r   r   r”   r   r   r   r   r   ry   ry   r   ry   )ry   r   ry   ry   r   ry   ry   r   r   ry   r”   r   r”   r   )r”   r   r”   r   r   r”   r   r   r   r   ry   r   ry   ry   )r”   r   r   r”   r   r   r”   r   r   r   r”   r   r   r”   )r   ry   ry   ry   r   r   r   ry   ry   ry   r   r”   r”   r   )r   r”   r”   r   r   r   r   r”   r   r   r   ry   ry   ry   )r   r”   r   r”   r   r   r   r   r”   r   r   r”   r   r”   )r   r   r”   r”   r   r   r   r   r   r”   r   r   r”   r”   )r   r   r   r   ry   ry   ry   ry   ry   ry   r   r   r   r   )r   r   r   r   r”   r”   r   r”   r   r   r   r   r   r   zv:14©r’  rz   r   ©r  c                 s   ó    | ]}|V  qd S rŒ   rp   ©rŽ   rß  rp   rp   rq   r“   Þ  ó   € z.test_minsolve_linear_system.<locals>.<genexpr>)TFc                 s   r  rŒ   rp   r  rp   rp   rq   r“   à  r	  c                      s   t td gˆ dS )Nry   )r  rœ   rp   ©Z_qrp   rq   r™   ä  s    z-test_minsolve_linear_system.<locals>.<lambda>c                      s   t td gˆ ddS )Nry   Fr   rœ   rp   r
  rp   rq   r™   å  ó    c                   S   s   t td ddS )Nry   Tr  rœ   rp   rp   rp   rq   r™   è  r‚  )rB   re   rf   rg   r]   rh   r<   r   r¨   r  r[   r¬   )ZpqtZpqfr  rz  rß  r{  r’   rp   r
  rq   Útest_minsolve_linear_system¿  sR   

884400ô&ÿ4
þþr  c                  C   s4   t ddd} tt| d | d  d ƒƒdksJ ‚d S )Nre   Trî   ru   rv   ry   )r   rÚ   rB   rà   rp   rp   rq   Útest_real_rootsë  s   (r  c                  C   sl   dt d  dt   dtd   d dt d  dt  t  dtd   d	 g} tt| tt d
dƒdks4J ‚d S )NicË†rt   iQÖAiTâkl   1ö'	 iýûa5iPQRiçäžl    d(	 FrÆ   r„   )re   rf   rÚ   rB   )r’   rp   rp   rq   Útest_issue_6528ñ  s   "&þ r  c                  C   s’   t ddd} td|  d ƒd tdd|   ƒd	 g}t|| ƒtjfgks&J ‚t|| dd
tjfgks4J ‚t|| dddtjftdƒfgksGJ ‚d S )Nre   Trî   r„   rÈ   ru   rv   râ   ry   ©rš  FrÜ  )r   r   rB   r   r´   )re   r’   rp   rp   rq   Útest_overdeterminedú  s
   (*r  c                  C   sÀ   t dƒ} td| d  d| d   ƒddt t tdƒ gks J ‚t ddd} td| d  d| d   ƒdgks9J ‚td	ƒttdƒƒ ttdƒƒ }td| d  dd|    ƒ| |gks^J ‚d S )
Nre   r„   rt   rv   r   Trî   ru   r‹   )r   rB   r   r   r$   r+   )re   r^   rp   rp   rq   Útest_issue_6605  s   8& .r  c                   C   s,   t td ƒsJ ‚t tƒrJ ‚t dƒrJ ‚d S )Nrt   T)rO   re   rp   rp   rp   rq   Útest__ispow  s   r  c               	   C   sä   t tt d t dt  tj d  ƒ t td  d t dtd  dtd   dt  d ƒd  tddƒ d td d t t dtd  dtd   dt  d ƒd  tddƒ d  ƒ } t| tddd}t|ƒdkspJ ‚d S )Nrt   r„   râ   ry   FrÇ  ru   )r+   rj   ri   r   r´   r   rB   rÚ   ©r   r®   rp   rp   rq   Útest_issue_6644  s*   8"ÿÿÿÿ"ÿÿÿÿÿr  c                   C   sd   t td t tt gttgƒddgksJ ‚t td tt  tt gttgƒdt t fgks0J ‚d S )Nrt   )r”   r”   r  )rB   r]   r^   r_   rp   rp   rp   rq   Útest_issue_6752  s   *:r  c                   C   s¶   t ttd d  td  td t d  ƒdddttd t d dƒttd t d dƒttd t d dƒttd t d dƒttd t d dƒttd t d dƒg	ksYJ ‚d S )	Nry   rt   r‹   r”   r   rv   r„   ru   )rB   re   rW   rp   rp   rp   rq   Útest_issue_6792  s
   *.((ýr  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 yTrî   rv   rt   ry   r<  )rz   rÈ   râ   rl   r”   r  r/  re   rØ   ©Z	imaginaryrŠ   c                      s   t tˆ ƒd ƒS rk  )rB   rª  rp   rà   rp   rq   r™   >  r‚  z6test_issues_6819_6820_6821_6248_8692.<locals>.<lambda>r~  r  r„   r   rz   r|   )r   rB   rª  r   r   r¡   r   r²   r   r   r   r+   r´   r!   r    r   r[   r€   r   r$   )rf   r   rØ   r~  r|   rp   rà   rq   Ú$test_issues_6819_6820_6821_6248_8692&  s>   ,(,&&
ÿ.
ÿ $:&6.,,0r  c                   C   s  t dtdt ƒ ttƒ tdt ƒd d  dktƒt tk ttdƒd k @ ks*J ‚t dtdt ƒ d ttd ƒ ttƒd d  dktƒt tk ttdƒd k @ ksVJ ‚t ttƒd td  tdt d ƒ ttƒd d  dktƒt tk ttk @ ks€J ‚d S )Nrt   r   r„   )rB   r#   re   r   r$   rp   rp   rp   rq   Útest_issue_17638V  s   TXXr  c                  C   s0  t dƒ\} }}}}}| d | | | |  | |  d ||  | |   }t dddd\}}}	|dd||    |	|    }
||
  ¡ }|t|ƒ ¡ 9 }t|| ƒ}| ¡ }|||	g}t||dd} t| ƒdkshJ ‚|||  |||   ||| |	|| ||  i}|D ]}| d |  ¡ ||  ¡ ks•J ‚qƒd S )	Nzs, tau_c, tau_1, tau_2, phi, Krt   ry   zK_C, tau_I, tau_DT)r  Znonzerorw   r   )r   Ztogetherr@   r¢   r>   r‡  rB   rÚ   )rÏ   Ztau_cZtau_1Ztau_2ÚphiÚKÚtargetZK_CZtau_IZtau_DZPIDr   r_   ÚvarsZknownsolutionÚvarrp   rp   rq   Útest_issue_14607^  s,   ÿ6ÿ

þ"ÿr   c                     sd  ddl m‰ m‰ ttˆ dˆ   tˆ ƒ ˆ ƒˆ ƒˆ tˆ ƒhks!J ‚tˆ ˆ ƒg ks*J ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   ¡ƒt
dtj ƒd gksLJ ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   d d ¡ƒt
dttdƒ ƒ ƒd t
dttdƒƒ ƒd gksJ ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   ¡ƒt
dtdtdƒ ƒ ƒd t
dtdtdƒ ƒ ƒd gksµJ ‚ˆ tˆ ƒ d  ˆ ˆ tˆ ƒ ¡} t| ƒt
dtt
dƒ ƒ ƒgks×J ‚tt‡ ‡fdd„ƒ ddt
t	dƒ d ƒ t	dƒ g}tˆ d dˆ   ˆ ƒ|ksJ ‚ttdt	ˆ ƒ ˆ t	dƒ  ƒƒt|ƒksJ ‚tt
dˆ  ƒˆ ˆ ƒˆtˆƒ d gks0J ‚d S )	Nr   ©re   rf   ry   rt   rv   c                      s   t ˆ tˆ ƒtˆˆ  ƒ  ˆ ƒS rŒ   )rB   r3   r$   rp   r!  rp   rq   r™   ‡  rh  z+test_lambert_multivariate.<locals>.<lambda>rŠ   )ro  re   rf   rH   r>   r#   rJ   rB   rË   r$   r"   r   r  r+   r[   r€   r¡   )r   r‘   rp   r!  rq   Útest_lambert_multivariate{  s"   2D20ÿ*6ÿ $" .2r"  c                   C   sn   t dttƒ ttdƒ  tƒdgksJ ‚tt tt tt  ƒtƒtt tttƒ t ƒ ttƒ hks5J ‚d S rk  )rB   r3   re   r¡   r]   r"   r$   rp   rp   rp   rq   Útest_other_lambertŽ  s   ( ÿr#  c            
      C   sN	  t td t ttd t ƒ d ƒtddƒtddtdƒ  ƒd  tddƒtddtdƒ  ƒd  gks6J ‚t td t ttd t d ƒ d ƒtddƒtddtdƒ  ƒd  tddƒtddtdƒ  ƒd  gksnJ ‚t tt ttd ƒ tƒdtt d ƒ gks‡J ‚t tt ttd ƒ  t¡tƒdttdƒ ttƒ d ƒ dttdƒttƒ d ƒ gks¶J ‚t dt ttd ƒ  t¡tƒdttdƒ d ƒ dttdƒd ƒ dttdƒ d dƒ gksèJ ‚t tttƒ dt  d tƒtdttdƒ ƒ ƒgksJ ‚t td  dt  tƒdddttdƒd ƒ tdƒ gks&J ‚t td dt  tƒdddttdƒd ƒ tdƒ gksEJ ‚t dt d dd	t d   tƒ} t	| ƒdkr~| d
  
¡ td	dƒtdtddƒ tdƒ d ƒdtdƒ   ks€J ‚t dt d dtddt  ƒ  tƒtddƒtdttddƒƒ d ƒd  gks«J ‚t ttƒt  ttd d ¡ƒt ttdƒ d ƒ tdtdƒ ƒgksÒJ ‚tdt d  }t dt|ƒ tt|ƒ  | tƒ} dttƒ }tdƒt }td }|td| ƒ td  }|tddƒ d }| |t|| d  ƒ |t||d  ƒ |t|ƒ d gks1J ‚ttddƒƒ}td	 }dtddƒ  }dtddƒ t }|tddƒ |tddƒ  d }t dt|ƒ | tƒ} | |td| | ƒ d |t|||  ƒ |t|||  ƒ gksŒJ ‚tddd}ddd| d   d|  d }	t|	|tt|	ƒ|ƒƒtddƒtdtdƒ ƒdtdƒ   gksÄJ ‚tt dttƒ ttƒd  ƒƒtdƒtdttdƒ d ƒ tdƒ ƒhksìJ ‚t dttƒ dttƒ  ttttƒ ttƒ ƒ tƒtt tdtd  tdt ƒ ƒd  ƒt gks"J ‚t tt ttd ƒ  td¡tƒ} t tddƒ }tdƒt }|d }| dt|d ƒ dt|| d  ƒ dt||d  ƒ gksfJ ‚t dt ttd ƒ  td¡tƒdttddƒƒ dttddƒtdƒt d  ƒ dttddƒtdƒt d  ƒ dttddƒdƒ gks­J ‚t td td ttƒ  ttddtdtt d ƒ itdttd ƒ igks×J ‚t td td  td  tƒttdtdƒ d dttƒ d  tt tddƒ  ƒƒgksJ ‚t dtttƒd ƒd  dt  ƒttdƒ dƒd d gks)J ‚t dtdttƒ d ƒd  t ƒttdƒ dƒd d gksKJ ‚t dttd d ƒd  td  ƒt tdttdƒƒ ƒ t tttdƒ ƒd ƒ tdttdƒ ƒ ƒtdttdƒƒ ƒtdttdƒ dƒ ƒ tdttdƒ dƒ ƒgks¥J ‚d S )Nrt   ry   r”   r„   rv   rŠ   rz   ru   éûÿÿÿr   i ØÿÿrÈ   iëÿÿÿr‹   rd   TrŽ  r^  rw   )rB   re   r#   r   r+   r"   r]   r   r$   rÚ   rp  r*   rË   r   r^   r   rI   rH   r>   r¡   r1   r-   rg   rf   r   )
r‘   Úaxrù   rú   rR  rS  rT  rU  rd   r   rp   rp   rq   Útest_lambert_bivariate•  sÊ   "  
þ&  
þ28ÿþÿ
ÿ@>"2
ÿ$(
ÿ$ÿ"ý ý $ÿ&ÿ4,ÿ"ý 02ÿ
ÿ"(
ÿ8ÿ"ÿ"ÿ"úr&  c                   C   sŒ  t ttƒttƒ ƒdt tdt gksJ ‚t ttƒttƒ ƒdttddƒtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒt	 d  tdƒtdtdƒt	  ƒ d  ƒ gksJ ‚t ttƒttƒ ƒdt	t gks¯J ‚t dttƒ ttƒ tƒtt
jƒgksÄJ ‚d S )Nr   rt   rz   r”   ry   rv   )rB   r3   re   r4   r   r2   r/   r   r+   r   r   r´   r'   r(   r1   rp   rp   rp   rq   Útest_rewrite_trigñ  s    *@Dÿÿÿÿ
ý$.r'  c                  C   sø   ddl m}  tttƒ| tƒ ƒdttddƒtdƒd  tdtdƒ d ƒd  ƒ dttddƒtdƒd  tdtdƒ d ƒd  ƒ dttdƒ d tj	 tddtdƒ  ƒd  ƒ dttddtdƒ  ƒ d tdƒd  tj	 ƒ gkszJ ‚d S )Nr   ©Úsechrt   r”   ru   rz   )
Ú%sympy.functions.elementary.hyperbolicr)  rB   r'   re   r%   r   r+   r   r´   r(  rp   rp   rq   Útest_rewrite_trighþ  s   4422ür+  c                  C   s  t ttƒ tttdtd td     ƒ } t| tddttttt ƒ  ƒ ttttt ƒ  ƒgks4J ‚tttd ƒtddt  ƒ d ƒdtdtdƒ ƒttddƒƒ d  tdƒd  tdtdƒ ƒ ttddƒƒ d d tdƒd  gdtd	tdƒ d
 d  ƒd  tdƒd  dtd	tdƒ d
 d  ƒd  tdƒd  gfv s©J ‚tttdt ƒd ƒtttƒ d ƒ tdƒ ƒg ksÆJ ‚d S )Nr”   rt   T)Úforcerv   ry   rŠ   iôÿÿÿiÜÿÿÿr‹   )	rg   r$   re   rf   rB   r+   r#   r   r(   rc  rp   rp   rq   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 rl  )rB   r0   re   r   r+   rp   rp   rp   rq   Ú
test_atan2  s   .r.  c                   C   s„   t ttƒt tƒttƒgksJ ‚t ttƒt tƒttƒgks J ‚t ttƒt tƒttƒgks0J ‚t ttƒt tƒttƒgks@J ‚d S rŒ   )rB   r5   re   rf   r8   r6   r7   rp   rp   rp   rq   Útest_errorinverses  ó      $r/  c               	   C   sR  t dƒ} tdƒ|  td| d  ƒ | d tdƒtd| d  ƒ d   }t|| ddd }|tddƒtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ   ddtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ     ftddƒddtd	d
ƒtdƒt d  tddƒ    td	d
ƒtdƒt d  tddƒ  fhks§J ‚d S )Nrk   rt   ry   Tr    ru   rv   r”   éû   rÀ   éo   r<  r  )r   r+   rB   r   r   )rk   r   r®   rp   rp   rq   Útest_issue_2725   s,   @*ÿÿ$ÿÿÿÿÿ"ÿþr3  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:rry   Fr©  c                 S   s   g | ]}|  ¡ ‘qS rp   )Ú	count_ops)rŽ   rÏ   rp   rp   rq   rñ   8  r  z(test_issue_5114_6611.<locals>.<listcomp>iÆ  )r   r<   rB   rª   rô   r  )r^   r_   r`   ra   r|   r}   rc   rØ   r×  rb   rØ  rj   rn   rð   rd   ri   rÐ   r’   rß  r‘   rp   rp   rq   Útest_issue_5114_6611*  s   *@\Lý"r5  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 )Nrv   za:9ry   r  r<  rt   )ry   rt   ry   r„   )	r<   r   ZdetrP   rª   rö   r=   rQ   rR   )rj   rÏ   rp   rp   rq   Útest_det_quick;  s   ,r6  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 bTrî   rt   rv   r<  r  rü  r]  rp   rp   rq   Útest_real_imag_splittingG  s   $ÿ*r7  c                  C   sB   dt d  dt d   dt   d } tdd„ t| ƒD ƒƒsJ ‚d S )Nrz   rv   r„   rt   ru   c                 s   s    | ]
}t t |¡ƒV  qd S rŒ   )r   r   rï   r×   rp   rp   rq   r“   Q  rÉ  z"test_issue_7110.<locals>.<genexpr>)re   rÍ  rB   rÔ   rp   rp   rq   Útest_issue_7110O  s   $r8  c                   C   s*   t dt ddt   ƒdt gksJ ‚d S re  )rB   re   rU   rp   rp   rp   rq   Ú
test_unitsT  r¯  r9  c                  C   s¢   t dƒ\} }}td|d  | |d  |  | dƒ}t|d|d  ƒ}t| d| |d  ƒ}ttt|||ƒ| ||gdƒƒ}t|ƒttd	gd
gdggƒƒksOJ ‚d S )NzA,B,Vg®Gáz²ƒ@g     €C@r   r   g    d6 Ag    0Œ!A)r   r   r   z4442890172.68209z4289299466.1432z70.5389666628177)r   r   r<   rA   r   rq  )rz  r{  r¥  Úeq1Úeq2Úeq3r®   rp   rp   rq   Útest_issue_7547X  s   &
þÿr=  c                  C   s*   t ddd} tt| ƒd ƒdgksJ ‚d S )NrÐ   Trî   rt   r„   rü  )rÐ   rp   rp   rq   Útest_issue_7895d  rø  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 )Nr  Trî   rt   rˆ   rv   é¿   rÇ   i‡  r‹   FrÆ   )r   r+   r   rB   )re   rf   rð  rñ  r]   r^   r‘   rp   rp   rq   Útest_issue_2777i  s   8""r@  c                  C   s"   d} t t|  tƒd | ksJ ‚d S )Ng{[Rs±Ò8r   rœ   )Únumberrp   rp   rq   Útest_issue_7322w  s   rB  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”   ry   Úbisect)Úmethod)rA   re   rp   rp   rp   rq   r™   }  s    ztest_nsolve.<locals>.<lambda>c                   S   s(   t tt d tt tt ftttfdƒS )Nrv   )iÎÿÿÿr  )rA   re   rf   rg   rp   rp   rp   rq   r™   ~  s   ( c                   S   s   t tt tt fdƒS )Nr  )rA   re   rf   rp   rp   rp   rq   r™     r‹  )r[   r¬   r   rp   rp   rp   rq   Útest_nsolve|  s   rE  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 )
Nrv   ry   r„   ru   c                   S   s   t ttd  t d tddS )Nru   ry   F)Ú
incomplete)rB   r]   re   rp   rp   rp   rq   r™   ‡  rs   z.test_high_order_multivariate.<locals>.<lambda>c                    s   g | ]	}t ˆ d  |ƒ‘qS rP  rV   r×   ©r`   rp   rq   rñ     rš   z0test_high_order_multivariate.<locals>.<listcomp>rt   )	rÚ   rB   r]   re   r[   r€   rö   r   r´   rp   rp   rG  rq   Útest_high_order_multivariate‚  s   &&".$rH  c                   C   sX   t dt d ƒdgksJ ‚t dtd  d ƒdgksJ ‚t tdddƒddgks*J ‚d S )Nr   ry   rt   zx*(1/x**0 - x)F©Úevaluate)rB   re   r   rp   rp   rp   rq   Útest_base_0_exp_0’  s
   ÿrK  c                   C   sd   t dtd  tgƒtƒ ksJ ‚t dtt  tgƒtt hks J ‚t dttdƒ tgƒthks0J ‚d S )Nry   r   rv   )rS   re   r¡   rf   r*   rp   rp   rp   rq   Útest__simple_dens™  s   "$rL  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 )Nrv   ry   rÁ  rÂ  rt   rÃ  r¹  rÄ  FrÅ  )rÚ   rB   r+   rf   re   r   rp   rp   rp   rq   Útest_issue_8755Ÿ  s   *,ÿÿÿÿÿrM  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¿  rC  éÍ   éh   rt   Tr  c                 S   s   g | ]	}d d„ |D ƒ‘qS )c                 S   s   h | ]}t d d„ |D ƒƒ’qS )c                 s   s    | ]}|  d ¡V  qdS )rt   N)rm   r×   rp   rp   rq   r“   Â  rÙ   z7test_issue_8828.<locals>.<listcomp>.<setcomp>.<genexpr>rÞ  )rŽ   r×  rp   rp   rq   Ú	<setcomp>Â  rh  z-test_issue_8828.<locals>.<listcomp>.<setcomp>rp   )rŽ   rk   rp   rp   rq   rñ   Â  rš   z#test_issue_8828.<locals>.<listcomp>)re   rf   rg   r+   rB   )rú   Úy1Úr1rR  Úy2rS  Zy3Zr3rß  Úf1Úf2Zf3rv  Úg1Úg2Zg3rè  rz  r{  r|  rd   ri   rÐ   rp   rp   rq   Útest_issue_8828¨  s,   
$ $
$$


 rY  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 )Nrv   r‹   r   r$  r^  rz   r<  rt   r„   rO  ru   r¤   r”   ry   r5  )rB   r3   re   r   r   r   r$   r1   rp   rp   rp   rq   Útest_issue_2840_8155Æ  s   *,,*4((&&
÷
.ÿrZ  c                   C   s"   t ddtd   ƒdgksJ ‚d S r±  rœ   rp   rp   rp   rq   Útest_issue_9567Ö  s   "r[  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 )Nrt   rv   r„   r^  rz   )rB   re   r   r   r+   r)   rf   rÚ   rï  rp   rp   rq   Útest_issue_11538Ú  s   .22
ý*
ÿ r\  c                  C   s€  t dƒ\} }}}}}}d| |  ||  d| |  ||  d||  ||  || d  |d  ||d  |d  ||d  |d  g}t|| ||||||gdd}t|d  d ƒ}	td|d  ƒ}
tdd|d   ƒ}tdƒ| }tdƒ|
 }|| |	 ||	 ||	 |||||di| |	||	||	|||||di| | d |
d  ||d |
d  ||
|| d |d  || d |d  |di| | d |
d  ||d |
d  ||
 || d |d  || d |d  |di| |d |
d  || d |
d  ||
|| d |d  || d |d  |di| |d |
d  || d |
d  ||
 || d |d  || d |d  |digks>J ‚d S )	Nza,b,c,d,e,f,gry   rt   Trw   r‹   rv   r”   rü  )r]   r^   r_   r`   ra   r|   r}   Ztermsr®   rÏ   Ús2Zs3Zs4Zs5rp   rp   rq   Útest_issue_12114ê  s4   66ÿ &(ÿ((ÿ&(ÿ((ÿ÷r^  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$J ‚d S ri  )rB   r   re   rp   rp   rp   rq   Útest_inf	  s   r_  c                     sò   t dƒ‰‡fdd„tdƒD ƒ} tdƒ}tt| |ƒƒ}|d d… |dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}| d d… | dd … \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}|| d	   |¡ ¡ ||d	   ¡ kswJ ‚d S )
Nr|   c                    s   g | ]}ˆ |ƒ‘qS rp   rp   r×   rf  rp   rq   rñ   
	  r  z$test_issue_12448.<locals>.<listcomp>rl   zx:15rv   c                    óT   g | ]&}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS ©r„   ry   rt   rv   rp   r×   ©r_   re   rf   rg   rp   rq   rñ   	  ó    Lÿc                    r`  ra  rp   r×   rb  rp   rq   rñ   	  rc  r   )r   rö   r   rx   r¶  rB   Zxreplacer4  )Zfunr  r·  ZssymZsfunrp   )r_   r|   re   rf   rg   rq   Útest_issue_12448	  s&    ÿÿ ÿÿÿrd  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 )Nrt   ry   )rT   re   rf   rg   rp   rp   rp   rq   Útest_denoms	  s     ".,2re  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 x5rt   rv   r‹   ry   rz   r”   r   ru   )r   r   r   r´   r+   rB   )rù   rú   rR  rS  rT  rU  ru  Zsolsrp   rp   rq   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rf  c                  C   s:   t dƒ} t| tdƒtdƒ  tdƒ | f| ƒg ksJ ‚d S )Nrh   ru   rt   rü  )rh   rp   rp   rq   Útest_issue_13849:	  s   2rg  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kilorâ   iÀàÿÿ)Úsympy.physics.unitsri  rj  rB   re   rf   rh  rp   rp   rq   Útest_issue_14860?	  s   0rl  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”   ry   rt   r   rz   r<  rü  )rb   rc   r]   r^   rp   rp   rq   Útest_issue_14721D	  s*   ..ýý þý0ÿÿ"ÿÿ0rm  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 )
Nre   Trî   r„   é‚   rt   iA  i  r  )r   rB   r+   r   rà   rp   rp   rq   Útest_issue_14779R	  s   0ÿÿÿÿro  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 )Nrt   rv   FrI  rŠ   r„   r”   iá0  iÕW i¢éÿÿrz   râ   r  r£   r@  )rB   rf   r	   re   r   r   )r:  r;  rp   rp   rq   Útest_issue_15307X	  s    ÿ
ÿ 
ÿ" rp  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 )Nrv   rt   ry   )rB   re   r   rf   rp   rp   rp   rq   Útest_issue_15415d	  s
   02>rq  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 )Nrt   rÈ   r  r  r–   ry   )rt   rv   r„   ru   r‹   rÈ   r„   rz   r‹   rv   r+  râ   r<  ru   r^   r”   TrŽ  )rB   r   re   r+   r   r´   r   r$   r   r   r   )r^   rp   rp   rq   Útest_issue_15731l	  s4   >",F," (,D*Fÿ($D"""&rr  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 )Nr„   rê  rv   rt   ró  )rB   re   rf   r   rp   rp   rp   rq   Útest_issue_10933Œ	  s   ,rs  c                  C   s,   t ddd} tt| t ƒ| ƒdgksJ ‚d S )Nre   Trî   r   )r   rB   rª  rf   rà   rp   rp   rq   Útest_Abs_handling‘	  s    rt  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 )Nre   rt   ru   rÇ   r   g      ø?rv   g)\Âõ( @g=
×£p=L@éj   ry   )r   rB   r   Úfalserà   rp   rp   rq   Útest_issue_7982–	  s   4Jrw  c                  C   sP   t dƒ\} }t| | |  | | | |  | g| |gƒ||d  |fgks&J ‚d S )Nr  ry   râ  r!  rp   rp   rq   Útest_issue_14645ž	  s   Drx  c                  C   sR   t dƒ\} }ttd| dk f| | dkfƒ| ƒ|td| dk f| dfƒigks'J ‚d S )Nr  r¦   rê  T)r   rB   r,   r!  rp   rp   rq   Útest_issue_12024£	  s    ÿry  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 )NrÈ   r  iõÿÿÿ)rB   re   r   r+   r$   r   r#   r"   rp   rp   rp   rq   Útest_issue_17452©	  s   4
ÿPrz  c                   C   s0   t tttdƒd  ƒt  t tƒg ksJ ‚d S r®  )rB   r5   re   r   r   r   rp   rp   rp   rq   Útest_issue_17799¯	  rå   r{  c                  C   sN   t ddd} ttt| d d ƒ|  ƒ|  ƒddtdƒ dtdƒ gks%J ‚d S )Nre   Trî   rt   ry   r”   )r   rB   rª  r+   rà   rp   rp   rq   Útest_issue_17650³	  s   Br|  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 )Néøÿÿÿrt   r<  ry   r„   rv   )re   r   rL   rc  rp   rp   rq   Útest_issue_17882¸	  s   Hr~  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 rg  )rB   r#   re   rp   rp   rp   rq   Útest_issue_17949½	  r0  r  c                   C   s  t tttdƒdƒƒddgksJ ‚t tttdƒttdƒ tƒƒg d¢ks%J ‚t tttdƒdƒƒddgks5J ‚t tttdƒ tƒttdƒ gksHJ ‚t tttdƒ ttdƒ ttƒ tƒttƒ ttdƒ ttdƒ gksmJ ‚t td ttd dƒ tƒg d¢ksJ ‚d S )Nrt   rv   rz   )r^  r   ry   r   ry   )rz   r”   rv   )rB   r   r   re   Úpowr]   rf   r3   rp   rp   rp   rq   Útest_issue_10993Ä	  s    * &J,r  c                  C   sr   t t d } t t }t| |gt tƒt t tdt iksJ ‚t d t }t| |gt tƒt dt tdt iks7J ‚d S )Nry   r”   rt   rz   )re   rf   r
   rB   r   )r:  r;  r<  rp   rp   rq   Útest_issue_11553Í	  s
   &,r‚  c                  C   s¼  t dƒd } tttƒd ttƒd  ƒ tdttƒd  dttƒd   ƒtd|  ƒtd|  dtdƒt   d ƒ td|  dtdƒt   d ƒ gksOJ ‚t j}tttƒd ttƒ ƒdt| tdƒd  tdƒtdtdƒ ƒ d  ƒ dt|tdƒd  tdƒtdtdƒ ƒ d  ƒ dttdƒ d | tdƒtdtdƒ ƒ d  ƒ dttdƒ tdtdƒ ƒ d | tdƒd  ƒ gksÉJ ‚tdttƒ ttƒ ƒtdƒgksÜJ ‚d S )Nry   rv   ru   r„   rt   rz   )	r   rB   r1   re   r3   r/   r+   r   r´   )rh   rc   rp   rp   rq   Útest_issue_19113_19102Õ	  s   "* 
þ4244
ü*rƒ  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 )Nrv   r„   ru   râ   ry   rt   )r   r+   rB   re   ©r]   r^   r_   r`   rp   rp   rq   Útest_issue_19509ä	  s   ür…  c               	   C   sò   t dƒ\	} }}}}}}}}|| | |  | }	d|d | d  | dt||	 ƒ   }
||||	t|
ƒ    }dt|| | ||| | |  |   ƒ dt||| | |  |  ƒ  }| |d|   |d|   d g}t||ƒ|kswJ ‚d S )NzTHT HT DBH dib c0 c1 c2 c3 c4ry   )r   r#   r$   rB   )ZTHTZHTZDBHZdibZc0Úc1Úc2Úc3Zc4r|   Úrhsr   Útermr®   rp   rp   rq   Útest_issue_20747ï	  s   (*ÿ"r‹  c                  C   s0  t dt  d  } t|  t dt d i¡ t¡dktƒtdƒtk ttdƒd k @ ks+J ‚t|  t dt d i¡ t¡dktƒtdƒd tk ttdƒd k @ ksPJ ‚t|  t dt d i¡ t¡dktƒtd	ƒd tk ttdƒk @ kssJ ‚t|  t dt d i¡ t¡dktƒtdƒtk ttdƒd k @ ks–J ‚d S )
Nry   rt   rv   r   r”   r^  rz   r„   r$  )rh   rB   rË   re   r   r   rf  rp   rp   rq   Útest_issue_20902ú	  s
   FJFJrŒ  c                  C   sÀ   t ddd} tttdƒƒ ttt| ƒƒ tttƒ g}t|tttƒttdƒƒtt| ƒƒtttdƒƒƒfgks8J ‚t	tƒt	t ƒ ttƒt	tƒt	t ƒ   t d g}t|tƒtdiks^J ‚d S )Nr]   Trî   r„   ru   )
r   re   r&   r1   rf   r'   rg   r(   rB   r#   )r]   r‰  Z	newsystemrp   rp   rq   Útest_issue_21034
  s
   *:6r  c                  C   sÔ   t ttd t d  td td   td  ƒ t d td   } tt t d td   }t||   t t   ||  ft||   t t   ||  fg}ttd td  td  t t tt  t gttƒ|kshJ ‚d S rg  )r]   r+   rk   r^   r_   rB   re   rf   )rg   rh   r®   rp   rp   rq   Útest_issue_4886
  s   @<@rŽ  c                  C   sT   t ddd\} }}}t| |t  ||t   tƒt||  ƒt|| ƒ gks(J ‚d S )Nry  TrŽ  )r   rB   re   r$   r„  rp   rp   rq   Útest_issue_6819
  s   @r  c                  C   s0   t dƒ} td|  t d | ƒdt gksJ ‚d S )Nre   ry   r„   )r   rB   r   rà   rp   rp   rq   Útest_issue_17454
  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 )Nr0  rt   )r+   rB   re   )r¼   rp   rp   rq   Útest_issue_21852
  s   ,r‘  c                  C   sŒ   t  ttdt   tdt  dt   ddt    } t| tddd}|ttdt   tdt   t dt   t ddt   gksDJ ‚d S )Nry   FrÇ  )r`   r]   r_   ra   r^   rB   r  rp   rp   rq   Útest_issue_21942#
  s   6
ÿÿ
ÿr’  c                  C   sP   t td td  t d dd} t td td  t d dd}| |ks&J ‚d S )Nru   rt   ry   F)ZcubicsTrœ   )r*   Zradrp   rp   rq   Útest_solver_flags*
  s     r“  c                  C   s’   dt d  dtd d  td   } t|  ¡ t dddt td d  tdtdƒt   td d  t dtdƒt   td d  gksGJ ‚d S )	Nrt   rv   r¤   ry   r‹   Fr©  r”   )re   rf   rg   rB   rp  r+   r   rc  rp   rp   rq   Útest_issue_227680
  s   $0 ÿÿr”  c                   C   sZ   t td  ttd t ƒ d dt t dt t  fƒtdttitdttigks+J ‚d S )Nrt   rz   r”   ry   )rB   rf   r$   re   r   rp   rp   rp   rq   Útest_issue_227177
  s   8ÿr•  c                  C   s²  t dt td tt t t   td dt dtddƒ t  dt  t dtddƒ t  dt  t   td ddtddƒ  t t	dƒt  dtddƒ t  dt  t	dƒt  ddtddƒ  t  dtddƒ t  dt    td dt	dƒ t ddtddƒ  t  t	dƒt  dt	dƒ t  t	dƒt  ddtddƒ  t    tdt dt  dt	dƒ t  dt	dƒ t    d ƒ} t
| ttttttgtƒttddƒttdd	ƒttd
dƒddtddƒ  d  ddtddƒ  d	  tddtddƒ  d dt	dƒ d  ddtddƒ  d  ttd
dƒddtddƒ  d	  ddtddƒ  d  tdt	dƒ d ddtddƒ  d  ddtddƒ  d  iksWJ ‚d S )Nr}  ru   r„   rt   rv   r^  râ   r$  i  iØÿÿÿé   ry   iìÿÿÿrˆ   i  iöÿÿÿrÇ   )r   r]   re   r^   r_   ra   r   r`   rb   r+   rG   rc  rp   rp   rq   Útest_issue_10169<
  sV   Fÿÿÿÿ&ÿÿ
ÿÿÿÿÿF
ÿÿý ÿüû

6<6<úr—  c                  C   s:  t dƒ\} }}}t| ttƒ |ttƒ  |tt| ƒ ƒ t¡jdd}t|||ftƒ}||dt	| t
| d |d  ƒ | ƒ || d  | t
| d |d  ƒ  |d  | t
| d |d  ƒ  i|dt	| t
| d |d  ƒ | ƒ || d | t
| d |d  ƒ  |d  | t
| d |d  ƒ  d igks›J ‚d S )NzA, B, r, phiT)Ztrigrt   r”   )r   r   r3   rh   r1   Zrewriter   rp  rG   r/   r+   )rz  r{  rÐ   r  r   rt  rp   rp   rq   Ú*test_solve_undetermined_coeffs_issue_23927M
  s   8$Bþ$Dþýr˜  N)rl   (  Zsympy.assumptions.askr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.functionr   r   r   Zsympy.core.mulr	   Z
sympy.corer
   r   Zsympy.core.numbersr   r   r   r   r   r   Zsympy.core.relationalr   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   r   r   Zsympy.core.sympifyr   Z(sympy.functions.combinatorial.factorialsr   Z$sympy.functions.elementary.complexesr   r   r   r    r!   Z&sympy.functions.elementary.exponentialr"   r#   r$   r*  r%   r&   r'   r(   Z(sympy.functions.elementary.miscellaneousr)   r*   r+   Z$sympy.functions.elementary.piecewiser,   Z(sympy.functions.elementary.trigonometricr-   r.   r/   r0   r1   r2   r3   r4   Z'sympy.functions.special.error_functionsr5   r6   r7   r8   Zsympy.integrals.integralsr9   Zsympy.logic.boolalgr:   r;   Zsympy.matrices.denser<   Zsympy.matricesr=   Zsympy.polys.polytoolsr>   Zsympy.printing.strr?   Zsympy.simplify.radsimpr@   Zsympy.solvers.solversrA   rB   rC   rD   Zsympy.solversrE   rF   rG   Zsympy.solvers.bivariaterH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rk  rU   Zsympy.polys.rootoftoolsrW   Zsympy.testing.pytestrX   rY   rZ   r[   Zsympy.core.randomr\   rÌ   ro  r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rr   r~   rƒ   r…   r†   r‡   r‰   r°   r½   r¾   rÁ   rÂ   rÃ   rÒ   rÓ   rÕ   rÜ   rÝ   rÞ   rß   rá   rã   rä   ræ   rç   ré   rë   rí   rý   r[  r\  rs  rw  rx  r}  rƒ  rˆ  rŠ  r  r‘  r“  r”  r•  r–  rž  r   r¡  r¨  r«  r¬  r­  rÏ  rÐ  rÑ  rÔ  rÕ  rÖ  rÙ  rä  rå  rç  ré  rî  rö  r÷  rù  rú  rý  rÿ  r  r  r  r  r  r  r  r  r  r  r  r   r"  r#  r&  r'  r+  r-  r.  r/  r3  r5  r6  r7  r8  r9  r=  r>  r@  rB  rE  rH  rK  rL  rM  rY  rZ  r[  r\  r^  r_  rd  re  rf  rg  rl  rm  ro  rp  rq  rr  rs  rt  rw  rx  ry  rz  r{  r|  r~  r  r  r‚  rƒ  r…  r‹  rŒ  r  rŽ  r  r  r‘  r’  r“  r”  r•  r—  r˜  rp   rp   rp   rq   Ú<module>   s’    (0D
h$


7
v3('-
,



  7


+D	(,	
0

[



	

		