a
     ¬<b(u 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$l|m}Z}m~Z~mZm€Z€mZm‚Z‚mƒZƒm„Z„m…Z…m†Z†m‡Z‡mˆZˆm‰Z‰mŠZŠm‹Z‹ d<d&d'„ZŒd(d)„ Zd*d+„ ZŽd,d-„ Zd.d/„ Zd0d1„ Z‘d2d3„ Z’d4d5„ Z“d6d7„ Z”d8d9„ Z•d:d;„ Z–d<d=„ Z—d>d?„ Z˜d@dA„ Z™dBdC„ ZšdDdE„ Z›dFdG„ ZœdHdI„ ZdJdK„ ZždLdM„ ZŸdNdO„ Z dPdQ„ Z¡dRdS„ Z¢dTdU„ Z£dVdW„ Z¤evdXdY„ ƒZ¥dZd[„ Z¦d\d]„ Z§d^d_„ Z¨d`da„ Z©eudbdc„ ƒZªddde„ Z«dfdg„ Z¬dhdi„ Z­djdk„ Z®dldm„ Z¯dndo„ Z°dpdq„ Z±drds„ Z²dtdu„ Z³dvdw„ Z´dxdy„ Zµdzd{„ Z¶d|d}„ Z·ewd~ƒdd€„ ƒZ¸dd‚„ Z¹dƒd„„ Zºeud…d†„ ƒZ»eud‡dˆ„ ƒZ¼evd‰dŠ„ ƒZ½d‹dŒ„ Z¾ddŽ„ Z¿dd„ ZÀeud‘d’„ ƒZÁd“d”„ ZÂd•d–„ ZÃd—d˜„ ZÄd™dš„ ZÅd›dœ„ ZÆddž„ ZÇdŸd „ ZÈd¡d¢„ ZÉd£d¤„ ZÊd¥d¦„ ZËd§d¨„ ZÌd©dª„ ZÍd«d¬„ ZÎd­d®„ ZÏd¯d°„ ZÐd±d²„ ZÑd³d´„ ZÒdµd¶„ ZÓd·d¸„ ZÔd¹dº„ ZÕd»d¼„ ZÖd½d¾„ Z×d¿dÀ„ ZØevdÁdÂ„ ƒZÙeudÃdÄ„ ƒZÚdÅdÆ„ ZÛevdÇdÈ„ ƒZÜdÉdÊ„ ZÝdËdÌ„ ZÞdÍdÎ„ ZßdÏdÐ„ ZàdÑdÒ„ ZádÓdÔ„ ZâdÕdÖ„ Zãd×dØ„ ZädÙdÚ„ ZådÛdÜ„ ZædÝdÞ„ Zçdßdà„ Zèdádâ„ Zédãdä„ Zêeudådæ„ ƒZëdçdè„ Zìdédê„ Zídëdì„ Zîeudídî„ ƒZïeudïdð„ ƒZðdñdò„ Zñdódô„ Zòeudõdö„ ƒZód÷dø„ Zôdùdú„ Zõdûdü„ Zödýdþ„ Z÷dÿd „ Zødd„ Zùdd„ Zúdd„ Zûdd„ Züd	d
„ Zýeudd„ ƒZþdd„ Zÿdd„ Z dd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd „ Zd!d"„ Z	d#d$„ Z
d%d&„ Zd'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;S (=  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   úp/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/solvers/tests/test_solvers.pyÚNS-   s    rr   c                  C   s   t tdƒ\} }| tƒ|tƒ }}t|t d || d g|t|ƒ||d t| d iks\J ‚t||t  d ||gddd |d|diksŽJ ‚t||d t  t ||gdd|t|d t  igksÊJ ‚t| dƒd td gddtd	| dƒdigksüJ ‚d S )
NÚ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     ÿ2<r~   c              	   C   s.   zt | |ƒ W dS  ttfy(   Y dS 0 d S )NTF)rB   Ú	TypeErrorÚNotImplementedError)ÚeqÚsymbolrp   rp   rq   Úguess_solve_strategy;   s
    
rƒ   c                   C   s  t tdƒtƒsJ ‚t ttƒs J ‚t tt tƒs2J ‚t dt tƒsDJ ‚t ttdƒ tƒsZJ ‚t tdtddƒ  tƒsvJ ‚t td d tƒsŒJ ‚t td d tƒs¢J ‚t tt t tƒs¸J ‚t tttƒ t tƒsÒJ ‚t ttd  td tdtd  ƒ  tƒsJ ‚d S )Né   rt   ry   rv   )rƒ   r   re   r]   r+   r   rf   r#   rp   rp   rp   rq   Útest_guess_polyC   s    $ÿr…   c                   C   sv   t ttƒd tƒsJ ‚t ttddƒ ttƒ d tƒs:J ‚t dt dttƒ  tƒsXJ ‚t tdt  t tƒsrJ ‚d S )Nry   rv   r„   )rƒ   r+   re   r   rf   rp   rp   rp   rq   Útest_guess_poly_cvS   s    ÿr†   c                   C   s€   t td td d  tƒsJ ‚t ttd  td tdtd  ƒ  tƒsLJ ‚t ttƒd ttddƒ ttƒ d  tƒs|J ‚d S )Nry   rt   rv   )rƒ   re   rf   r+   r   rp   rp   rp   rq   Útest_guess_rational_cv^   s
    $ÿr‡   c                   C   sœ   t ttƒd tƒsJ ‚t dttƒ t tƒs0J ‚t ttƒtt ƒ t tƒsPJ ‚t dt d tƒsfJ ‚t dt  d tƒs~J ‚t ttt  t tƒs˜J ‚d S )Nry   rt   rv   é
   )rƒ   r#   re   r1   rf   r]   r^   rp   rp   rp   rq   Útest_guess_transcendentali   s    ÿr‰   c               	      sX  t dtdi‰ t dt  d dt  dt  d f‰t‡ ‡fdd„ttttfD ƒƒsTJ ‚ttˆŽ t tƒˆ kslJ ‚ttt d d	 ƒƒt	dƒt	dƒ hks–J ‚tt t d
 t t d gƒt d	tdiksÂJ ‚tt t
t ƒ t ddt
t ƒgksæJ ‚tdƒtdt ƒ  krg ksn J ‚tddgƒg ks$J ‚ttdƒgt gƒg ks@J ‚tt d
 td ft tt ƒt d
tdikslJ ‚ttd
 thƒd
gksˆJ ‚ttd
 t thƒtd
igksªJ ‚tt t d
 t tgƒd
t tfgksÔJ ‚tt t d
 t tgddt d
t igksJ ‚tt t d
 ƒt d
t igks&J ‚tttt   d ttgƒtdtdiksRJ ‚tt t  td  d ttf} t| Ž tdƒ tdƒftdƒtdƒ fgks¢J ‚t| ddiŽttgtdƒ tdƒftdƒtdƒ fhfksâJ ‚t| ddiŽttdƒttdƒ ittdƒ ttdƒigks"J ‚tt d  tt   t t t d d	t t  d	 t  }tdd}t|tttgfdtttgi|¤Žtttd d	t   tt dt  tdd	t  igksÀJ ‚| tdd¡ t|tttgfdtttgi|¤Žtd	t t td  d	t  tt dt  tdd	t  igks4J ‚ttt  td t d	   d
t   d	t   ttddttd  t  d
t d
   dt d   d	t   d t d t d	   igks¶J ‚tddt  t t
tƒ  ƒg ksÜJ ‚ttdd„ ƒ ttt
t ƒt  gƒt tdƒ tdiksJ ‚tt
t ƒt  t
tƒt fƒt tdƒ ttdƒ iksPJ ‚ttt
t ƒt  gt tƒtdt tdƒ iks€J ‚tt d t tƒt d gks¢J ‚tg t gƒg ks¸J ‚tt t d d	 t t d gƒt t d igksîJ ‚tt t d dt  dt  d	 fƒt t d iks&J ‚ttt d dƒƒdgksDJ ‚tdtt dƒgt gddt digksnJ ‚ttt t ƒtt dƒtt t d ƒgt gddg ks¤J ‚ttt t d ƒt dk gt ƒrÆJ ‚ttt dƒt d dk gƒtt dƒksðJ ‚ttt t ƒtt t d ƒgt ƒg ksJ ‚tdt ƒg ks,J ‚tt d dgt gddg tƒ fksTJ ‚d S )Néýÿÿÿry   ru   rt   é   rl   c                 3   s"   | ]}t |ˆƒttƒˆ kV  qd S ©N©rB   re   rf   )Ú.0Ú	container©ÚansÚeqsrp   rq   Ú	<genexpr>y   ó    z"test_solve_args.<locals>.<genexpr>r„   rv   éÿÿÿÿT©Zimplicité*   rz   rw   r   Úsetrx   ÚexcludeF©Úsimplifyé   é   c                   S   s$   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   Ú<lambda>¨   r”   z!test_solve_args.<locals>.<lambda>ç        ©r˜   )re   rf   ÚallÚtupleÚlistr˜   Ú	frozensetrB   r   r   r#   r+   r]   r^   r_   rc   rd   rb   rx   Úupdater[   r€   r"   r   r   )Úargsr   Úflagsrp   r   rq   Útest_solve_argsu   s€    $
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0"68*6"*(r¨   c                  C   sÎ  t dt d tƒtddƒgks"J ‚t tdt dƒtƒtddƒgksFJ ‚tt td d tƒƒtj tjhksnJ ‚tt ttd dƒtƒƒtj tjhks˜J ‚t ttd  tƒtd gks¸J ‚ttdƒ} t ttd  tƒ| |  d t	dƒt
 |  d  |  d t	dƒt
 |  d  gksJ ‚tdƒ\}}}}}}t |t |t  | |t |t  | gttƒt|| ||  || ||   t|| ||  || ||   iks¦J ‚ttjttji}t tt tt fttƒ|ksØJ ‚t tt tt fttfƒ|ksüJ ‚t tt tt fttgƒ|ks J ‚tt td dt  d tƒƒddtj  tdƒddtj  hksfJ ‚tt td d d t tƒƒt	dt	tƒ ƒt	dt	tƒ ƒ t	dt	tƒ ƒt	dt	tƒ ƒ hksÊJ ‚d S )Nrv   rt   ry   úa11,a12,a21,a22,b1,b2rl   r„   rz   )rB   re   r   r   r˜   r   ÚOnerf   r*   r+   r   r   ÚZeroÚHalfr]   )ÚrxÚa11Úa12Úa21Úa22Úb1Úb2Úsolutionrp   rp   rq   Útest_solve_polynomial1Å   s:    "$(* 
:ÿ.  þÿ
"$$ýÿÿrµ   c                   C   s   t dtƒg ksJ ‚d S )Nr„   ©rB   re   rp   rp   rp   rq   Útest_solve_polynomial2é   s    r·   c                   C   s´   t ttƒd tƒdgksJ ‚t ttƒd tƒdgks8J ‚t ttddƒ d tƒdgksZJ ‚t ttddƒ d tƒdgks|J ‚t ttƒttddƒ  ttddƒ  tƒdgks°J ‚dS )	zŽ
    Test for solving on equations that can be converted to a polynomial equation
    using the change of variable y -> x**Rational(p, q)
    ry   rt   r„   r   rv   é   r   N)rB   r+   re   r   rp   rp   rp   rq   Útest_solve_polynomial_cv_1aí   s
    ""r¹   c                   C   sj   t tdt dtttƒ   tƒƒtjdtd  hks8J ‚t ttttdƒd  tƒƒtjtdƒhksfJ ‚d S )Nr„   ry   rt   rv   r¸   )r˜   rB   re   r]   r+   r   r«   r*   rp   rp   rp   rq   Útest_solve_polynomial_cv_1bù   s    8rº   c                   C   sv   t tdt  d tƒtjttdƒ d  tjttdƒ d  gtjttdƒ d  tjttdƒ d  gfv srJ ‚dS )z‰
    Test for solving on equations that can be converted to a polynomial equation
    multiplying both sides of the equation by x**m
    ry   rv   rt   N)rB   re   r   r¬   r   r+   rp   rp   rp   rq   Útest_solve_polynomial_cv_2þ   s
    **ÿÿr»   c                  C   s  t d dt d   dt d   dt   d } t| dd	}|D ]&}|  t | ¡ ¡ ¡ }t|d
ƒs<J ‚q<t d dt d   dt d   dt   d } t| ƒ}|D ]}|jtksœJ ‚qœttt d dt d   d ƒd
 ddtt d dt d   d d
ƒ ¡ ksþJ ‚d S )Nru   én   rv   é7   rt   i	  iÓ  F©Úcheckr   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    ,,	& ÿrË   c               
   C   s®  t d dt   d } t| dd}|D ]&}|  t | ¡ ¡ ¡ }t|dƒs$J ‚q$t d dt d   dt d   d	t   d
 } t| ƒ}|D ]}|jtks„J ‚q„tt d dt d   dt d   t  d ƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒtt d dt d   dt d   t  d dƒgksªJ ‚d S )Nru   rl   rœ   Fr¾   r   rv   rt   rˆ   rÀ   r‹   ry   r„   )re   rB   rÄ   rn   rÅ   rÆ   rW   rÇ   rp   rp   rq   Útest_quintics_2  s     ,*,,,,,ûrÌ   c                  C   sF   t d t d  dtddƒ  } t| ƒt|  ƒ  kr<g ksBn J ‚d S )Nru   rv   rt   ry   )re   r   rB   ©rf   rp   rp   rq   Útest_quintics_33  s    rÎ   c                  C   s>   t td dt  d ƒ} tdd„ | D ƒƒr6t| 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“   ;  r”   z&test_highorder_poly.<locals>.<genexpr>)rB   re   r¡   Úlen)Úsolrp   rp   rq   Útest_highorder_poly8  s    rÔ   c                   C   s<   t ttd  td tdtd  ƒ  tƒtd gks8J ‚dS )z!Test solve for rational functionsrv   rt   ry   N)rB   re   rf   r+   rp   rp   rp   rq   Útest_solve_rational>  s    rÕ   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_conjugateC  s    rÖ   c                   C   sˆ   t td td  ttddtt ittigks2J ‚t td td ttƒ  ttddtt tttƒƒ itttttƒƒ igks„J ‚d S )Nrt   Trw   )rB   re   rf   r#   r+   rp   rp   rp   rq   Útest_solve_nonlinearG  s    26ÿr×   c                  C   sl   t dƒ} tt| d d| d d   dd| d d   ƒ| ƒg ksDJ ‚tt| d|   d|  ƒ| ƒg kshJ ‚d S )Nre   rt   ry   r„   )r   rB   r   ©re   rp   rp   rq   Útest_issue_8666M  s    <rÙ   c                   C   s:   t ddtd  dt   d tƒtddƒtjgks6J ‚d S )Nr„   rt   é   rŠ   )rB   re   r   r   r¬   rp   rp   rp   rq   Útest_issue_7228S  s    rÛ   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$   re   r+   rp   rp   rp   rq   Útest_issue_7190W  s    rÜ   c                  C   s<   t dƒ} | t| d d ƒ }| | ¡}t|| ƒg ks8J ‚d S )Nre   rt   ry   )r   r+   r   rB   )re   r|   Zf_diffrp   rp   rq   Útest_issue_21004[  s    
rÝ   c                  C   s²  t dƒ\} }}}}t| d | | | d|  |d g| |gƒg ksDJ ‚t| d | | | d|  | d g| |gƒg ksvJ ‚t| d | d | | | d|  g| |gƒg ks¨J ‚t| d|  d d|  d|  d g| |ƒ| d|diksäJ ‚tdd||d  |d d dg|d |d d	| d |d  dgg d
¢gƒ}t|| |||ƒ| || d  | ||| d  | |diksrJ ‚t| | | | | | g| |||ƒ| | || iks®J ‚d S )Nzx, y, z, t, nry   rt   ru   rŠ   r‹   rl   r   rz   )r•   r   ry   r   r   )r   rB   r<   rE   )re   rf   rg   rh   rn   ÚMrp   rp   rq   Útest_linear_systemb  s    222<"þ*ÿ
rß   c                  C   sF   t g d¢g d¢g d¢g d¢gƒ} t| tttƒtdtdtdiksBJ ‚d S )N)r   g      .@ç      $@g     à…@)ry   ry   ry   g      Y@)r   rà   g      @g      i@)g      Àr   r   r   r   g      NÀg      d@)r<   rE   re   rf   rg   )rÞ   rp   rp   rq   Útest_linear_system_xfailv  s    ýrá   c                  C   sš   t dƒ} t| ddƒ| ddƒ | ddƒ | ddƒ | ddƒ | ddƒ g| ddƒ| ddƒ| ddƒ| ddƒƒ| ddƒ| ddƒ | ddƒ| ddƒ iks–J ‚d S )Nr]   r   ry   )r   rB   )r]   rp   rp   rq   Útest_linear_system_function  s    > ÿ&ÿrâ   c                  C   s2   dd„ } t ddƒD ]}| |ƒ\}}t||ƒ qd S )Nc           
         sÔ   d|  d }t ddd\‰ }}t d | ¡dd}t d | ¡dd}t d |d ¡dd}t‡ fd	d
„t|ƒD ƒƒ}g }t| ƒD ]L}	| | ˆ |	¡ ˆ |i¡||	  ¡ | | ˆ |	¡ ˆ |i¡||	  ¡ q~||fS )Nrt   ry   z	x, x0, x1T©Úrealzy0_:{}zy1_:{}zc_:{}c                    s   g | ]\}}|ˆ |  ‘qS rp   rp   )rŽ   ÚoZcoeffrØ   rp   rq   Ú
<listcomp>’  r”   zMtest_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqs.<locals>.<listcomp>)r   ÚformatÚsumÚ	enumerateÚrangeÚappendr   rÄ   )
ZwyÚorderÚx0Úx1Zy0sZy1sr_   Úexprr’   rÑ   rp   rØ   rq   Ú_mk_eqs‰  s    $&z9test_linear_system_symbols_doesnt_hang_1.<locals>._mk_eqsry   rÚ   )rê   rB   )rð   rn   r’   r_   rp   rp   rq   Ú(test_linear_system_symbols_doesnt_hang_1‡  s    rñ   c               '   C   s  t g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d	¢g d
¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢g d¢gƒ} tdƒ }\}}}}}}}}	}
}}}}}}}}}}|tdƒ d |tdƒ d |tdƒ d |tdƒd |tdƒ d |tdƒd  |td!ƒ d |	td"ƒ d# |
td$ƒd |td%ƒ d |td&ƒ d |td'ƒ d( |td)ƒd( |td*ƒ d |td+ƒd, |td-ƒ d |td.ƒd  |td/ƒ d |td0ƒd i}t| t |d1 ƒ ƒ}t||ƒ|ksÔJ ‚td2ƒ}t||  t |d1 ƒ ƒ}t||ƒ|ksJ ‚d S )3N)éB   é   é'   é2   éX   é(   é%   é`   r   éA   é   é   rø   éH   r   é   r½   rø   é   éL   )rˆ   é]   é"   éb   é;   é,   éC   éJ   r  é^   éG   é=   é<   é   r‹   rt   é9   rÚ   é   éN   )rþ   é[   r  é   é@   rú   ró   é5   éM   r  éU   é:   éW   rô   rô   rÁ   é$   r  r  rv   )r  éF   rl   r  éD   é+   éV   éS   éQ   rý   é   é.   r  é   r  r  r  rô   é?   r‹   )éE   r÷   r  é   r  r÷   r!  r  r  r  r   éY   é>   rû   é   é&   é   rÀ   rœ   r  )rõ   é   r  r   r  é-   rþ   r   rÿ   rÿ   rü   éc   éa   éR   rÚ   r   r,  r  r  é#   )r  r)  r+  rö   rˆ   r  é	   r  éZ   r.  r!  é)   r  r  r+  r  r*  rö   ró   rô   )r—   r$  r  r  r‹   é!   r  r  r  rl   r  éK   r  r!  r  r  r&  rý   rÀ   ró   )rÁ   rÚ   rt   rý   r	  é4   rù   ru   é    é3   rû   r  éO   rö   r  r  r  é   r3  r  )rþ   rû   r'  r  r  rô   r"  rÿ   rþ   rœ   r   é1   rø   rò   r(  r  rv   r	  r
  r7  )r  r.  éP   r:  r9  r  ry   rø   rt   r  é6   r.  r9  é/   r<  r0  r/  r   r,  r÷   )rl   r:  r.  r  r  r  r+  r  r+  r-  rl   r  é0   r5  rò   ró   r&  r<  r-  rø   )r&  r  éI   r  r5  r  rÿ   r(  r   r  é\   r(  r-  r  r	  r  r9  r1  r  r+  )rt   r6  r  ró   r	  rø   r  r	  ru   r2  r-  rú   r  r  rú   r+  r  rö   r#  rõ   )r÷   é8   ry   r  r8  r  r8  r&  rø   rÿ   r+  r=  rv   ry   r6  r  r  r/  éT   r6  )r3  rl   r  r8  rú   r0  é   r"  ró   rþ   r   rÿ   r  rÀ   r  rù   rB  r  r  ry   )r-  r)  rœ   r5  ry   rt   rõ   rC  r5  r   rþ   r.  r2  r?  r7  r8  r  rv   r.  rù   )r÷   rÿ   r5  rˆ   rˆ   r	  rA  r  r.  ru   r  r>  ry   r9  r   r)  rõ   r   r  r5  )r(  r%  r  r  r  r5  r1  r  r  r   r  rÀ   r  rö   r>  rù   rö   r  rC  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   r£   rB   r   )rÞ   Úsymsrí   rî   Úx2Úx3Úx4Úx5Úx6Úx7Úx8Úx9Úx10Zx11Zx12Zx13Zx14Zx15Zx16Zx17Zx18rÓ   r’   rf   rp   rp   rq   Ú(test_linear_system_symbols_doesnt_hang_2¤  s^    í2írO  c               
   C   s–   t dƒ} tg d¢ddd|  dgdd| d dggƒ}t|tttgƒtd| d d	|    tdd
|  | d d	|     td|  | d d	|    iks’J ‚d S )Nrn   )ry   rt   r   ry   ry   rv   rt   r„   r•   rŠ   r)  rœ   r‹   )r   r<   rF   re   rf   rg   )rn   rÞ   rp   rp   rq   Útest_linear_systemLUÛ  s    *"þrP  c                     s  ddl m} m} tttƒd tƒtdƒgks0J ‚tt| t | ttƒd  tƒƒ| |  tdƒhkshJ ‚tttƒt	 tƒt
t	ƒ dt  t
t	ƒgks˜J ‚tdttƒ t	 tƒt
t	d ƒ dt  t
t	d ƒgksÔJ ‚ttttƒttƒƒtƒtd gksúJ ‚ttttƒtt ƒ t	 tƒƒtt	d tt	d d ƒd  ƒtt	d tt	d d ƒd  ƒhtt	tt	d d ƒ ƒtdƒ tt	tt	d d ƒ ƒtdƒ htt	d tt	d t	d  ƒd  ƒtt	d tt	d t	d  ƒd  ƒhfv sæJ ‚tttƒd tƒtdƒgksJ ‚ttttƒdƒtƒtdƒgks,J ‚tttƒd tƒtdƒgksNJ ‚ttdt ƒd tƒtddƒgksvJ ‚tdtd  tƒg ks’J ‚tddt  tƒg ks®J ‚ttdt  tƒttdƒƒ tdƒ gksÞJ ‚tdt d tdt d ƒ tƒtddƒtdttddƒƒ d ƒd  gks0J ‚tdt tdt ƒ tƒttddƒƒd gksdJ ‚ttdt d	 d	ttƒ  tƒƒtd
ƒtd	ƒtt  hks¤J ‚dtdt d ƒ d ‰ tˆ tƒ}t|ƒdkrìt‡ fdd„|D ƒƒsðJ ‚tdtdt d ƒ d tƒttddƒƒd d gks,J ‚tttƒd tƒtt gksNJ ‚ddt d d  dddt d    ‰ tˆ tƒ}tdƒ }dtddƒ }tdd| d  ƒ}tdƒ}tdƒ}|t|d ƒ }	|d }
ddtdƒ  }| }|t|d ƒ }|d }||dt||	 |
  ƒ   ||dt||	|
  ƒ   ||dt|||  ƒ   ||dt|||  ƒ   ||dttdd| d  ƒ ƒ   g}||ks¦J |ƒ‚tˆ  ¡ tƒ|ks¾J ‚ttttƒ t	 tƒt
t	t ƒ dt  t
t	t ƒgksüJ ‚tttdt ƒ t	 tƒt
t	t ƒ d t t
t	t ƒd gksBJ ‚tttttƒƒ t	 tƒttt
t	t ƒƒ tt
t	t ƒdt  ƒt tt
t	t ƒdt  ƒ tt
t	t ƒƒgks¸J ‚ttttƒ tƒtd ttddƒ gksæJ ‚tt	|t | t   tƒ|  t	 t	|  g| t	 |t	  gfv s,J ‚tt	|t| t ƒ  tƒ| tt	| ƒ gks^J ‚tt	|d| t    tƒ|t	 | t	  gt	| | t	   gfv s¤J ‚tt	| t|   tƒt	|  d|  gksÒJ ‚ttt t	 tƒtt	ƒttƒ gksüJ ‚tdt d tƒdtdƒtdƒ  gks*J ‚ttt	 ƒtdit	digksLJ ‚ttt	 gƒtdit	digkspJ ‚ttt	 d ƒtdit	digks–J ‚ttt	 d gƒtdit	digks¾J ‚ttt	 td t	d   ƒtditt	 itt	it	digksþJ ‚ttt	 td t	d   gƒtditt	 itt	it	digk	s@J ‚tttdƒt ƒdt  tƒdgk	sjJ ‚tttdƒt ƒttdƒt ƒ tƒdgk	sœJ ‚tdƒ‰tt	ˆtdƒt ƒ t	ˆtdƒt ƒ  tƒdgk	sÞJ ‚tˆtƒˆdƒ tƒdgk
s J ‚tˆtƒˆdt ƒ tƒdgk
s&J ‚tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ ttdd„ ƒ ttdd„ ƒ ttttƒƒƒdtd gk
s¬J ‚tdddd\} }ttt| d tt| ƒd  ƒ|ƒƒd!k
sìJ ‚tt	dt  t tƒtt	ƒttƒ gksJ ‚d S )"Nr   ©r]   r^   rv   rt   r„   r   ru   iíÿÿÿrÚ   éüÿÿÿc                 3   s&   | ]}ˆ   t|¡jd ddkV  qdS ©T)Zchopr   N©rÄ   re   rn   ©rŽ   r]   ©r   rp   rq   r“     r”   z,test_solve_transcendental.<locals>.<genexpr>ry   r‹   rÁ   r0  ia	  rÀ   rˆ   r|   c                      s   t ˆ ttƒˆ ddƒ tƒS ©Nry   rt   r   rp   ©r|   rp   rq   rž   D  r”   z+test_solve_transcendental.<locals>.<lambda>c                      s   t ˆ ttƒˆ dt dƒ tƒS ©Nrt   r   rp   rX  rp   rq   rž   E  r”   c                      s   t ˆ ttƒˆ dt ƒ tƒS ©Nry   r   rp   rX  rp   rq   rž   F  r”   c                      s   t ˆ ttƒˆ dƒ tƒS rZ  r   rp   rX  rp   rq   rž   G  r”   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   rž   M  s    c                   S   s   t td t t d tƒS ©Nrt   rv   r   rp   rp   rp   rq   rž   Q  r”   za, bTF)rä   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$   r˜   r1   rf   r-   r   r   r3   r+   r   r"   r   r   rÒ   r¡   Úexpandrg   r.   r   r[   r€   Ú
ValueErrorr   Ústr)r]   r^   r‘   Úresultrí   rî   rF  rG  rH  rI  rJ  rK  rL  rM  rN  rp   )r   r|   rq   Útest_solve_transcendentalè  s¸     80<&þþ""þú	"$"(0 (ÿ
4@
*<"(

$ü>F,&þ.F2F.*."$&(@B*2:"&""ÿ
rd  c                  C   s€  t dƒ} tdƒ| ƒ}tdƒ| ƒ}tdƒ\}}}}}}t|| ||  | || ||  | g||ƒ}	|	||| ||  || ||   ||| ||  || ||   iks°J ‚t|d |ƒdgksÈJ ‚td| d |ƒtddƒgksêJ ‚t|| | ¡ || | ¡  | || | ¡ || | ¡  | g| | ¡| | ¡ƒ}	|	| | ¡|| ||  || ||   | | ¡|| ||  || ||   iks˜J ‚t| | ¡d | | ¡ƒdgks¾J ‚td| | ¡ d | | ¡ƒtddƒgksîJ ‚d| d d| d h}
t|
||hƒ|tddƒ|diks,J ‚t dƒ}td	ƒ}|d ||ƒd  d|  d }t| |¡t||ƒ|ƒƒ| d ||ƒ gksJ ‚t dƒ}tdƒ| ƒ}t|| || | ¡  | || || | ¡  | g|| | ¡ƒ}	|	| | ¡|| ||  || ||   ||| ||  || ||   iks:J ‚t dƒ}td	ƒ}t||ƒ |¡||ƒ |d¡ d ||ƒ |¡||ƒ |d¡ g||ƒ |¡||ƒ |d¡ƒ}	|	||ƒ |d¡d
||ƒ |¡d
iksÔJ ‚t||ƒ |d¡||ƒ |d¡ d d||ƒ |d¡ ||ƒ |d¡ d||ƒ |d¡ g||ƒ |d¡||ƒ |d¡ƒ}	|	||ƒ |d¡d||ƒ |d¡diks|J ‚d S )Nrh   re   rf   r©   ry   rv   rt   r„   r|   r^  r   )r   r   r   rB   r   r   )rh   re   rf   r®   r¯   r°   r±   r²   r³   ZsolnÚeqnsr|   ÚFrp   rp   rq   Ú$test_solve_for_functions_derivatives_  sn    0  þ
",ÿÿÿ(&ÿ&0& 4 ÿÿ
ÿ( ÿ@ÿ,6ÿÿÿrg  c                  C   st   t dƒ} td | tƒd  dt  d }| t¡}t|| tƒ t¡ƒdt | tƒ gtd | tƒ  gfv spJ ‚d S )Nr|   rt   r„   ry   )r   re   r   rB   )r|   rf  ra   rp   rp   rq   Útest_issue_3725’  s     
rh  c               	   C   s|  t dƒ\} }}}tdd| |||gƒ}tddg d¢ƒ}tddg d¢ƒ}t|| | | |||gƒ| d|tddƒ|d|diks|J ‚t|| | g| |||gƒ| d|tddƒ|d|diks¶J ‚tt|| |ƒ| |||gƒ| d|tddƒ|d|diksðJ ‚t|| ||  g| |||gƒ| ||tddƒ| iks,J ‚t|| ||  g| |||gƒ| || |tddƒ| ikslJ ‚t|| ||  || ||  g| |||gƒ| ||d	|d	iks°J ‚tt|| || ƒg| |||gƒ| ||tddƒ| iksîJ ‚tt|| || ƒg| |||gƒ| || |tddƒ| iks0J ‚tt|| || ƒt|| || ƒg| |||gƒ| ||d	|d	iksxJ ‚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_3870™  s    8::<@D>Brm  c                  C   sV  t dƒ} tttƒdksJ ‚tttgddks0J ‚tt| gddksFJ ‚tttdt  ƒttd ftdt ffv stJ ‚tttdt  tgdtdt fksœJ ‚tdt t dƒttd ftdt ffv sÊJ ‚tdt t dtgƒttd fksðJ ‚tdt t dtgƒtdt fksJ ‚ttd t dƒttd fks<J ‚t| tƒ| tft| ffv s\J ‚tttƒd ttƒd  d t ƒtd	ttƒd  ttƒd  fks¦J ‚tttƒd ttƒd  d t tgddksÚJ ‚tttdƒƒtdfksöJ ‚tddt d  ƒd
ksJ ‚ttd tt ƒ tgdtdfks>J ‚ttd ttƒ tgdtd ttƒ dfksrJ ‚ttttd  ƒ tgdtdfksœJ ‚tdt d ƒdt d dfksÂJ ‚tddtd   ƒtdfksäJ ‚tttƒd  tttƒd   t }t|ƒdksJ ‚ttƒd ttƒd  }t|ƒdksDJ ‚tt	dd„ ƒ d S )NÚw©r   ry   ©r™   ©r   rt   rv   r   ry   rz   ©r   r   r•   c                   S   s   t ttdƒdƒS r[  )rC   r   re   rp   rp   rp   rq   rž   Æ  r”   z#test_solve_linear.<locals>.<lambda>)
r   rC   re   rf   r1   r3   r   r#   r[   ra  )rn  r   rp   rp   rq   Útest_solve_linear¬  s6    .(.&($ "ÿ
4*4*&"$rs  c                   C   s&  t ttd  ttd   tt  dt t  t d tttgtƒtdtdtdiksVJ ‚t tt ttd   dt d td t   ttgtƒtdtdiksžJ ‚t td t td  td t td   td t t  td d t t  td d  td  tttgtƒtdtdtdiks"J ‚d S )Nrt   ry   rz   r•   )rG   r]   re   r^   r_   rp   rp   rp   rq   Útest_solve_undetermined_coeffsÉ  s&    @ÿ6
ÿ(ÿÿ
ÿÿ
ÿþrt  c               
   C   s   t dƒ} ttj| k | tk ƒ}t| d dkƒ|ks4J ‚t| d dkgƒ|ksNJ ‚t| d dkg| ƒ|ksjJ ‚t| d dkg| gƒ|ksˆJ ‚t| d d dƒt| d d dƒg}t|ƒttttt	dƒ | ƒt| dƒƒttd| ƒt| t	dƒƒƒƒt
ddƒƒksüJ ‚t ddd} t| d d dƒt| d d dƒg}t|ƒtttt	dƒ | ƒt| dƒƒttd| ƒt| t	dƒƒƒƒksrJ ‚t| d | d  dk | ƒttd| ƒt| dƒƒks¨J ‚t| | d  dk| ƒttt | ƒt| dƒƒksÜJ ‚tt| ƒtjkƒttd	 | k | ttd
d	ƒ k ƒksJ ‚tt
d| dk ƒƒtj| k| tk @ ks>J ‚tt
d| dk ƒƒt | k | dk @ kshJ ‚tt
| dk dƒƒtj| k| tk @ ks’J ‚tt
| dk dƒƒt | k | dk @ ks¼J ‚tt
d| ƒƒdksÔJ ‚tt
d| ƒƒdgksîJ ‚tt
d| ƒƒdksJ ‚tt
d| ƒƒdgks J ‚tt
d|  ƒƒdks:J ‚tt
d|  ƒƒdksTJ ‚ttd| ƒƒdkslJ ‚ttd| ƒƒ| t k| tk @ t| dƒ@ ksœJ ‚d S )Nre   ry   rt   r   r•   Trã   rv   r‹   ru   F)r   r:   r   r«   r   rB   r   r   r;   r+   r   r3   r¬   r   r   rª   r   )re   rÓ   Úsystemrp   rp   rq   Útest_solve_inequalitiesÕ  sD    $ÿÿÿ$6ÿ
648****rv  c               	      sÒ  t dt ƒg ksJ ‚t tddt   ƒdgks2J ‚t tttƒ d ƒdgksPJ ‚t dt  dt d  ddt   ƒg ks~J ‚t td  dt  td d  d ƒg ks¬J ‚t ttd  d d ƒg ksÌJ ‚t tttd d ƒ tƒdgksðJ ‚t ttƒt tƒttƒgksJ ‚t ttƒƒg ks(J ‚t td t ttƒd  ttƒd  d tƒddgddgfv slJ ‚dddt d   d	 ‰ t ˆ tƒ} t| ƒdkr´t	‡ fd
d„| D ƒƒs¸J ‚t ttd ƒtd ttƒ  ttddttgttttƒttd ƒ ƒfttttƒttd ƒ ƒ fhfks(J ‚t td t
d  t
d td   ƒtt ittit
digksjJ ‚t td ddtd    ƒg ksJ ‚t ttt
  t tƒdgks²J ‚ttdd„ ƒ ttdd„ ƒ d S )Nry   ru   rt   rv   rz   r   r•   r„   rÁ   c                 3   s&   | ]}ˆ   t|¡jd ddkV  qdS rS  rT  rU  rV  rp   rq   r“   	  r”   z"test_issue_4793.<locals>.<genexpr>Tr    c                   S   s   t ttƒttƒ tƒS rŒ   )rB   r$   re   r#   rp   rp   rp   rq   rž     r”   z!test_issue_4793.<locals>.<lambda>c                   S   s   t dt ttƒ d ƒS r\  )rB   re   r#   rp   rp   rp   rq   rž     r”   )rB   re   r+   r#   rf   r$   r3   r1   rÒ   r¡   rg   r[   r€   ©r‘   rp   rV  rq   Útest_issue_4793ü  s,    .. $"D
*&8þB&"rx  c                  C   s<  t ttƒƒt ttd ƒƒ  kr*dgks0n J ‚t ttd ƒƒdgksJJ ‚tdƒ} t d|  ttƒ tƒg kspJ ‚t dt td  d tƒdgks”J ‚tt td dt   t¡ƒƒtjtdƒhksÄJ ‚td	ƒ}t dd
t |tƒ  |tƒ |tƒƒtt	d
dƒ gksJ ‚t dt
d
t d
ƒ d tƒt	ddƒgks6J ‚t ttƒtttƒƒ d ƒt	ddƒtdƒd  d gkstJ ‚tt ttttƒƒttt ƒƒ d ƒƒƒttdƒ d d ƒttdƒd d ƒhdttdƒ d ƒ dttdƒd ƒ htdtdƒ d ƒtdtdƒ d ƒhfv sJ ‚tt tttƒtt ƒ d ƒƒƒttdƒ d ƒttdƒd ƒhkshJ ‚tt tt tdt   d tƒƒt	ddƒtd
ƒd  dt  t	ddƒtd
ƒd  dt  hksÌJ ‚t ttt ƒtt t ƒ d tƒtt tdƒ gksJ ‚t tt tt  d tƒtdƒttƒttƒ  gtdƒttt ƒ gfv sXJ ‚tj}t tdt ƒtdƒ tƒdt|t	ddƒtdƒt d   ƒt|t	ddƒtdƒt d   ƒgdt| d tdƒ| t d  ƒt| d tdƒ| t d  ƒgfv s
J ‚tddd}t d| d |d  ƒg ks8J ‚d S )Nrv   r   ry   r]   rŠ   rt   rÁ   rC  r|   ru   r0  i´~ûÿi©æ  r„   r•   r!  rR  rd   T©Úpositive)rB   r+   re   r   r˜   r   r   r«   r   r   r*   r>   r#   r$   rf   rg   ÚExp1r   )r]   r|   r   rd   rp   rp   rq   Útest_PR1964  sF    0$0<.>(((&ýÿ
  ÿ
 :ÿ
<ÿ.ÿ
DDþr|  c                  C   s”  t ddd} t| d d | ƒg ks&J ‚t dddd}t|d |d  d| d  |ƒdgks`J ‚t ddd} t d	ƒ}t| d
|  d d|  d|  d g| |ƒg ks¨J ‚t| | | |d  d | |ƒtdƒtdƒ fgksàJ ‚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sJ ‚d S )Nre   Trã   rt   ry   rn   )Úintegerrz  ry  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_5197A  s    ,48@r~  c                   C   s¸   t ttttt   tddƒttƒtjttƒ hks8J ‚t ttttt   tddƒttƒttƒ hkslJ ‚tddt d  dtd  d fƒg ks˜J ‚tddt d  ƒg ks´J ‚d S )NFr¾   Try   rt   rv   )r˜   rB   re   rf   r+   r   r«   rp   rp   rp   rq   Útest_checkingS  s    ÿÿ4,r  c               	   C   s€  t ttd d ƒd ƒtdƒtdƒ gtdƒ tdƒgfv s@J ‚t dttd t ƒ d td d  tƒtttdtt tdƒ  ƒ ƒ tttdtt tdƒ  ƒ ƒgks°J ‚tdƒ\} }t	dƒ}t | |td   t|tƒ ƒ |tƒƒttd | td  |  ƒgksJ ‚t
dƒ}tj}t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv sŽJ ‚t t|d	 td  ƒ| tƒtd
|d	  ƒ td
|d	  ƒgtd
|d	  ƒtd
|d	  ƒ gfv söJ ‚t dt|dtd   ƒ tƒt| | ƒ d t| | ƒd gt| | ƒd t| | ƒ d gfv sfJ ‚t |d d t|t ƒt|t ƒ  tƒt d|  gks¦J ‚t dt|t ƒt|t ƒ  tƒtdƒ| gksÜJ ‚tt dt|t ƒt|t ƒd   tƒƒtdtdƒ ƒ| ttdƒ d ƒ| ttdƒ d ƒ| tdtdƒ ƒ| hks\J ‚t ttƒd ƒtdƒgks|J ‚d S )Nrt   ry   ru   rl   zC1 C2r|   r]   r„   rŠ   r•   rv   rz   )rB   r+   re   r#   rf   r$   r   r   r   r   r   r   r{  r3   r1   r'   r&   r˜   r/   r4   )ZC1ZC2r|   r]   r   rp   rp   rq   Útest_issue_4671_4463_4467]  s>    &ÿ
(>ÿ
L$$þ  þ$$þ@6(&&ÿÿ
r€  c               	   C   sL  t dƒ\} }tt| td  td  t|ƒtt  gttgƒƒt| t|ƒd  ƒ dt| t|ƒd  ƒ t|ƒ ft| t|ƒd  ƒt| t|ƒd  ƒt|ƒ fhks¨J ‚tttƒt	tƒ dt d gttgƒt
t	tddƒƒƒtddƒfgksðJ ‚tttƒt	tƒ dttƒ d gttgƒt
t	t
dƒƒ ƒt
dƒ fgks>J ‚ttttƒt	tƒ td d gttgƒƒt
t	dƒ ƒtdƒ ft
t	dƒƒtdƒfhksšJ ‚ttƒd t	tƒ td  dttƒ d g}t|ddttgt
dƒ ttdt ƒ t	t
dƒƒ ƒft
dƒ ttdt ƒ t	t
dƒƒ ƒ fhfks2J ‚t|ttddttgtttdt ƒ t	tƒ ƒftttdt ƒ t	tƒ ƒ fhfksŽJ ‚tt|ttƒƒt
ttd  t	t
dƒƒ ƒ ƒt
dƒ ft
td  t	t
dƒƒ ƒd t
dƒ fhksöJ ‚tt|ttƒƒt
dƒ ttdt ƒ t	t
dƒƒ ƒ ft
dƒ ttdt ƒ t	t
dƒƒ ƒfhks^J ‚ttƒd t	tƒ t dttƒ d g}t|ddttgt
dƒ tdt ƒ t	t
dƒƒ fhfksÆJ ‚t|ttddttgttdt ƒ t	tƒ fhfks J ‚tt|ttƒƒt
tt t	t
dƒƒ ƒ ƒt
dƒ ft
t t	t
dƒƒ ƒd t
dƒ fhks`J ‚t|ttƒtdt ƒ t	t
dƒƒ t
dƒ fgks˜J ‚tttd td  ƒtd	ƒ tt d fddttgtjtdƒftdƒtjfhfksòJ ‚ttttd td  ƒtd	ƒ tt d fttƒƒtjtdƒftdƒtjfhksHJ ‚d S )
Nzr,trt   r•   ry   rv   r„   Tr    rˆ   )r   r˜   rB   re   rf   r4   r+   r1   r#   r3   r$   r   r   rg   rª   )rÉ   rh   r’   rp   rp   rq   Útest_issue_5132z  sr    02ÿ.þÿ$ÿ(ÿ
(*ÿ
,
&(þÿ
<þ(&þÿ
(&þÿ
("ÿ ÿ$"þ
$ÿ
. ÿ2ÿr  c                  C   s´   t dƒ\} }}d}d}| dt  |dtd   t  |t d t  |dtd   t dt  |t  tt | g}tt|g}tt||dddƒdksšJ ‚tt||ƒƒdks°J ‚d S )Núlam a0 concç{®Gázt?çÌ«¢Ã;Êç?rt   ry   T)ÚmanualZminimal©r   rf   re   rÒ   rB   ©ZlamZa0Zconcr]   r^   r’   Úsymrp   rp   rq   Útest_issue_5335¦  s    ."
þ
r‰  ZHangsc                  C   sœ   t dƒ\} }}d}d}| dt  |dtd   t  |t d t  |dtd   t dt  |t  tt | g}tt|g}tt||ddƒdks˜J ‚d S )Nr‚  rƒ  r„  rt   ry   F©Zrationalr†  r‡  rp   rp   rq   Ú_test_issue_5335_float³  s    ."
þ
r‹  c                   C   sH   t ttd t d gtgƒƒtt d ƒ ftt d ƒfhksDJ ‚d S )Nrt   r„   )r˜   rB   re   rf   r+   rp   rp   rp   rq   Útest_issue_5767À  s     ÿrŒ  c                   C   sê   t ttd dt  d tt d gttgƒƒtjtdƒfdtdƒ dtdƒ fdtdƒ dtdƒ fhksnJ ‚ttd t d td t gƒg ks–J ‚ttd t d tt d gttfƒttd t d tt d gttfƒksæJ ‚d S )Nrt   rv   ry   ru   r„   )r˜   rB   re   rf   r   rª   r+   rp   rp   rp   rq   Útest_polysysÅ  s    ,"ÿÿ(,ÿÿ
ÿÿr  c            	   
      sf  t tdd„ ƒ t tdd„ ƒ tdtd‰‡fdd„} ‡fdd	„‰td
ƒd u sPJ ‚| tttƒƒtg fƒsjJ ‚| tttƒd
 ƒtd
 g fƒsŒJ ‚| tttƒttdƒ d ƒˆd ˆd  d ˆˆd t gfƒsÐJ ‚| tttƒttdƒ d ƒtd d g fƒsJ ‚| tttƒtd
 td
dƒ  ƒtd td
 d  g fƒs@J ‚| tttƒttd
 ƒ tdt ƒ ƒdtdƒ t dt  d
 g fƒsŒJ ‚| tttƒttd
 ƒ d ƒdt d g fƒsÀJ ‚| tttƒttd
 ƒ td
t ƒ ƒdtd  dt  g fƒsJ ‚| tt	ttƒ t
ttƒ  tttƒ  tttƒ  ƒt	ttƒ t
ttƒ  d tttƒ tttƒ  d  g fƒs|J ‚| tttƒtd
t ƒ ƒdt d
 g fƒs¬J ‚| tttƒtd
t ƒ d ƒtd t d g fƒsäJ ‚| tttƒtd
t ƒ tdt ƒ ƒdtd  dt  d
 g fƒs,J ‚tttƒtd
t ƒ tdt ƒ d ƒdtd  dtd   dtd   dt  d g fdtd  dtd   dtd   dtd   d g ffv sÆJ ‚tttƒtd
t ƒ tdt ƒ td
dt  ƒ ƒdtd  dtd   d td   d!t  d g fks4J ‚| tttƒttd
 ƒ ƒtjg fƒs^J ‚ttƒttd
 ƒ td
ttƒ ƒ }| t|ƒdtd  dt  g fƒsªJ ‚tt|d"d#ƒtjtddƒhksÐJ ‚t|ƒg ksâJ ‚ttttƒttd
 ƒ td
ttƒ ƒ ƒƒtjtddƒhks$J ‚| tttƒttd
 dƒ dttƒ  tƒtd$ƒg fƒs`J ‚| tttd
t  ƒtd
 td
dƒ  ƒtd td  td  dtd   t d
 g fƒs¾J ‚| tttd
t  ƒdttƒ  tƒdt t t dt  g fƒsJ ‚| tttƒtd
t ƒ d tƒtd t d g fƒs>J ‚tttttd ƒƒƒdgks`J ‚tttttd ƒ dƒƒdgks†J ‚ttd
ttdt d ƒ ƒƒg ks®J ‚ttttdt d ƒd tƒƒƒtj tdƒhksæJ ‚ttttdt d
 ƒttd ƒ dƒƒƒtdƒtd%ƒhks&J ‚ttttd& ƒd tdt ƒƒƒd'gksTJ ‚tdt d td
dƒ d ƒdgks~J ‚tttd
 ttd dtd   t dƒ ƒƒtd(dƒtd(dƒhksÆJ ‚tttdtd  d& ƒdt  ƒƒtdƒ tdƒhksJ ‚ttdt d ƒttd
 ƒ ttd ƒ ƒd)gks:J ‚tttd ƒtdt d
 ƒ dttd
 ƒ  ƒdgksvJ ‚tttƒttd& ƒ d* ƒdgksžJ ‚tttd ƒttƒ d ƒdgksÆJ ‚ttdtd  d ƒdt d  ƒd)gksöJ ‚tttƒd d ƒd+gk	sJ ‚tttd ƒttƒ d ƒg k	s<J ‚tttd
 ƒt d& ƒd,gk	s`J ‚tttd ƒd ƒd-gk	s€J ‚ttd.t ttd d ƒ ƒd& ƒdgk	s°J ‚tttƒttd
 ƒ tttƒƒ ƒg k	sÞJ ‚tdt d
 ƒttƒ tdd
t  ƒ }t|ƒd) }t|ƒg k
s$J ‚t|ƒg k
s6J ‚t|dt  ƒtd(d/ƒgk
sXJ ‚t|dt  ƒg k
srJ ‚tttd
 dƒttdƒ ƒtd td  dtd   dt  d
  g fk
sÂJ ‚| ttttdƒ ttdƒd  ttƒ tƒˆd ˆd  ˆ ttƒ ˆˆd t gfƒs J ‚| tttƒttdƒ t ƒˆd ˆd  t ˆˆd t gfƒsfJ ‚tttƒttdƒ d ƒd
gksŒJ ‚t td0d„ ƒ t td1d„ ƒ tttttdƒ ƒttt dƒ tƒtttd
dƒ t tddƒ  gksöJ ‚| tttƒttd
 dƒttd ƒ  d ƒˆd, dˆd   d2ˆd   d*ˆd   d3ˆd   d!ˆd   d4ˆd   d5ˆ  d6 ˆˆd t gfƒs”J ‚ttd
 dƒttdƒ }t|ƒdt d
 g fksÊJ ‚ttƒttd
 ƒ td
t ƒ dtdƒ d  }| t|ƒd7td  d8td   d9td   d:t  d; g fƒs>J ‚| tttdƒttdƒd  d
 ƒˆd ˆ d
 ˆˆd t gfƒs†J ‚| tttdƒttdƒd  d
 ƒtd dtd   t d
 g fƒsÎJ ‚ttd< ƒd u säJ ‚| ttttt dƒ ttt dƒd  ƒˆd ˆ t ˆˆd t t gfƒs8J ‚| ttttt dƒ ttt dƒd  tƒˆd ˆ t ˆˆd t t gfƒsŽJ ‚| ttttt dƒ ttt dƒd  tƒˆd ˆd  ˆ t ˆˆd t t gfƒsìJ ‚| tttd
 dƒttd
 dƒ tddƒ ƒˆd ddtd
dƒ  ˆd   ˆd  d,dtddƒ  ˆd   d,dtddƒ  ˆd   ddtddƒ  ˆ  d ˆˆd t d
 gfƒsªJ ‚t td=d„ ƒ tttdƒttdƒ d ƒd
gksàJ ‚ttƒttd
 ƒ td
t ƒ dtdƒ d  }| t|ƒdt d d>td  d?td   d@t  dA  g fƒsTJ ‚tdBƒ‰ t|ƒˆ ksnJ ‚| tttttd
 dƒ ƒttd
 dƒ d ƒˆd ˆd  dˆ  d ˆˆd t d
 gfƒsÒJ ‚ttd d
 dƒttd d
 dƒ d }| t|ƒˆd d,ˆd   dCˆd   dDˆd   dDˆ  dE ˆˆd td  d
 gfƒsZJ ‚ttttd
 dƒ ƒttd
 dƒ d }| t|ƒˆd dˆd   d&ˆd   dˆd   dFˆd   dˆ  d ˆˆd t d
 gfƒsêJ ‚| t|dGdHˆd dIˆd   dJˆd   dKˆd   dLˆd   dMˆ  dN ˆˆd t ttd
 ƒ gfƒs^J ‚| ttttttdƒd
 ƒ ƒttdƒ d ƒˆd* dˆd   dˆd&   dˆd   ˆd  dˆd   dOˆd   dPˆ  d. ˆˆd t gfƒsúJ ‚ttttƒdƒt ttd
 dƒ d
 ƒtdQ td ttƒd   dtd  ttƒd   dt ttƒd   ttƒd   g fks‚J ‚ttdRƒƒd u s˜J ‚| ttdRƒtƒˆdt  ˆ d
 ˆˆd t t gfƒsÖJ ‚tttjt  t tƒtd
t  td  g fksJ ‚ttttƒt td  d
 tƒƒdks8J ‚ttdStd  dTtd td
dƒ  td   dUtd tddƒ  t  dt  dV td"dWƒdks J ‚tdXƒ}t|tƒdtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd  td
ƒ d tdƒt d    dtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd  td
ƒ d tdƒt d    dtdƒd  d-t d-ttd ƒ  td
ƒd   tdƒ dY dZt d[ tdZƒd[  td
ƒd   gksJ ‚ttd
 dƒttdƒttdƒ  }| t|ƒdˆd%  dˆd/   ˆd  d
 ˆˆdQ t gfƒs„J ‚| t|d ƒdˆd%  dˆd/   dˆd,   ˆd  d*ˆd   dˆd   d*ˆd   d*ˆd   d& ˆˆdQ t gfƒsJ ‚| tttdƒttd
 dƒd  ttd dƒ ƒˆd\ˆd  d]ˆd   d^ˆd&   ˆd  d_  ˆˆd t d
 gfƒs†J ‚| tttdƒttd
 dƒ ttd dƒd  ƒd[ˆd%  d`ˆd*   dTˆd/   dZˆd,   daˆd   dbˆd   d_ˆd&   dcˆd   ddˆd   deˆ  ˆˆd t d
 gfƒsDJ ‚| tttdƒd ttd
 dƒ ttd dƒ ƒdeˆd%  ddˆd*   d_ˆd/   dZˆd,   dcˆd   dbˆd   dTˆd&   daˆd   d`ˆd   d[ˆ  ˆˆd t d
 gfƒsJ ‚| tttdƒd ttd
 dƒ ttd dƒ d ƒdeˆd%  dfˆd*   dgˆd,   dhˆd   diˆd   djˆd&   dkˆd   dlˆd   dmˆd   dnˆd   doˆd   dpˆ  dq ˆˆd t d
 gfƒsàJ ‚tttƒttd
 ƒ td
t ƒ tdt ƒ ƒ‰ tˆ ƒd
kr8tˆ d) ƒd d… drks<J ‚tdsƒ}|dt dt  ttd td  ƒ  }|tdd&ƒ tdƒ| dI  ‰ t|td"d#}t|ƒD ]F}ttt  t|¡ t¡td"d"dt}t‡ fdudv„|D ƒƒr  qòq d sòJ ‚tttd
 ƒttdƒ d ƒtdwƒksJ ‚ttttd
 ƒƒttd
dƒ  d ƒtdxƒksRJ ‚tttƒtttƒd
 dƒ d ƒtdyƒks‚J ‚tdzƒ}| t|ƒˆˆd  tdƒˆd  t  d{dtddƒ  dtd
dƒ  ˆd   d|d*td
dƒ  ˆd   d}dtddƒ  dtddƒ  ˆd  t  d~ˆd   d~tdƒ ˆd  t  dd€td
dƒ  ˆd   d dtdƒ t    ˆˆd d‚t  tdƒtdƒtd  d„t  d… ƒ  d† gfƒsºJ ‚t|ƒg ksÌJ ‚ttdƒttdƒ ttdƒ }| t|ƒˆdQ dˆd%   dˆd/   ˆd  t ˆˆdQ t gfƒs6J ‚ttdƒttdƒ ttt dƒ }| t|ƒˆt ˆd*  dˆd/  t  dˆd,  td   ˆd td   dˆd  td   dYˆd&  td   dˆd  td   dˆd  td   dˆd  td   td   ˆˆd tt  gfƒs.J ‚t td‡d„ ƒ tttd
ƒd   ttd
ƒd   dtd
ƒd   d(tdƒd  dtd
ƒd    ƒ}| t|ƒˆd  ˆd  dtd
ƒd   d(tdƒd  dtd
ƒd    ˆˆdQ t gfƒsôJ ‚ttƒd
 ‰tˆd ˆd  ƒtd dtd   dt  d g fks>J ‚tttd
  d d tƒd u sbJ ‚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   rž   Ñ  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   rž   Ó  s    rÈ   )Úclsc                    sd   t | d ƒt |d ƒksJ ‚|d r.ˆ | |ƒS | d  ¡ }|d  ¡ }||| fv ob| d |d kS ©Nry   r   )Úboolr`  )Úrvr‘   ra   r]   )Ús_checkrp   rq   r¿   Ú  s    
ztest_unrad1.<locals>.checkc                    sØ   t | ƒ} | d  t¡}t t|ˆ gt|ƒ ƒƒ}| d  |¡ ¡ | d d  |¡| d d  |¡gf} |d  |¡ ¡ |d d  |¡|d d  |¡gf}t| d ƒt|d ƒt|d  ƒfv oÖt| d ƒt|d ƒkS )Nr   ry   )r£   Úatomsr   ÚziprÒ   rÄ   r`  rb  )r’  r‘   r`   Úreps©rÈ   rp   rq   r“  â  s    66&ÿztest_unrad1.<locals>.s_checkry   rv   rt   r‹   ru   r  rz   r   r0  r„   r  ix  iè  ià  i  rÚ   iÜ  iæ	  i¼  é©   r2  r÷   éè   é    Fr¾   z32*sqrt(x)*(x + 1)**(1/3) + x - 4*y + (x + 1)**(2/3)r  rÁ   iúÿÿÿr•   r   rœ   r:  rˆ   r¸   r!  rü   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   rž   J  s    c                   S   s   t tdƒ ttƒt  ƒS rY  )rB   r+   r&   re   rp   rp   rp   rq   rž   M  r”   ró   r*  éÔ   éÀ   rA  i	=  iÈ£ im i { i  r^  c                   S   s6   t ttdƒttdƒ ttdƒ  ttd t d ¡ƒS )Nrt   rv   r„   ru   ry   )rL   r*   re   rÄ   rp   rp   rp   rq   rž   g  s    i5  iì  iÀ‰ i D z¥
        [4/5, -1484/375 + 172564/(140625*(114*sqrt(12657)/78125 +
        12459439/52734375)**(1/3)) +
        4*(114*sqrt(12657)/78125 + 12459439/52734375)**(1/3)]rô   r;  r'  r9  T)Z_reverserC  r?  é»   é  éä   r%  r  r6  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 - 1r$  i   iW  i   iÀ  r>  iÀ  iX  i+  iÐ  i¥  éØ   iÙ  iÚ  i@H  i¥ú iúí iÀê i Z	 iÕë2 i ` iÀÞl i@HM i©9  iÒ z0.73rf  ©r›   r¿   c                 3   s   | ]}|ˆ    ¡ jV  qd S rŒ   )r`  Úis_zerorU  rw  rp   rq   r“   Ì  r”   ztest_unrad1.<locals>.<genexpr>z_
        [(-11/(9*(47/54 + sqrt(93)/6)**(1/3)) + 1/3 + (47/54 +
        sqrt(93)/6)**(1/3))**3]a<  
        [(-sqrt(-2*(-1/16 + sqrt(6913)/16)**(1/3) + 6/(-1/16 +
        sqrt(6913)/16)**(1/3) + 17/2 + 121/(4*sqrt(-6/(-1/16 +
        sqrt(6913)/16)**(1/3) + 2*(-1/16 + sqrt(6913)/16)**(1/3) + 17/4)))/2 +
        sqrt(-6/(-1/16 + sqrt(6913)/16)**(1/3) + 2*(-1/16 +
        sqrt(6913)/16)**(1/3) + 17/4)/2 + 9/4)**3]z]
        [(-(81/2 + 3*sqrt(741)/2)**(1/3)/3 + (81/2 + 3*sqrt(741)/2)**(-1/3) +
        2)**2]a  
        -x + (1/2 - sqrt(3)*I/2)*(3*x**3/2 - x*(3*x**2 - 34)/2 + sqrt((-3*x**3
        + x*(3*x**2 - 34) + 90)**2/4 - 39304/27) - 45)**(1/3) + 34/(3*(1/2 -
        sqrt(3)*I/2)*(3*x**3/2 - x*(3*x**2 - 34)/2 + sqrt((-3*x**3 + x*(3*x**2
        - 34) + 90)**2/4 - 39304/27) - 45)**(1/3))é™   r7  éf   iT  i06  r)  i`2 i2  iìy  ix… i,ð  i*  c                   S   s&   t ttdƒttdƒ ttt dƒ ƒS )Nrv   ru   )rL   r*   re   rf   rp   rp   rp   rq   rž   ò  r”   ) r[   r€   r   r   rL   r+   re   r*   r   r]   r^   r_   rf   r`   r   rª   r˜   rB   r«   r   rN   r   rh   r&   r¬   rÒ   rr   r   ÚreversedrÄ   r   Úany)	r¿   r   rg   rd   ra   rf  ÚXÚxiÚYrp   )r‘   rÈ   r“  rq   Útest_unrad1Ï  s(   ÿ
ÿ"ÿÿ
ÿ
$ÿ
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&$ÿ*Nÿÿÿÿ
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*Bÿÿÿÿÿ
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Bÿÿ
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&F
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6,,ÿÿÿÿÿ
H
ÿ
ÿÿÿ
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ÿÿÿÿ
ÿÿÿ"ÿü"2ÿ
N
ÿÿÿÿ
.2ÿÿ
.:
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ÿÿÿÿÿ
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þþþþÿ

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,40Fÿ*ÿ
ÿþþþý"ÿÿÿýÿ
:ÿ
"Bÿÿÿÿþþþÿ
ÿVPÿ
>r¯  c                  C   s\   t dt ddtd   ƒ ƒtdt ddt ddtd   ƒ  ƒ   } t| ƒtjgksXJ ‚d S )Nry   r„   rt   )r+   re   rB   r   r¬   rV  rp   rp   rq   Útest_unrad_slow   s    Dr°  c                   C   s¬   t ttd dtd   dƒd t ƒtddƒgks6J ‚t ttd dƒttd d dƒ d ƒddttd td  dtd   dtd   dt  d d	ƒd  gks¨J ‚d S )
Nrv   rt   ry   ru   r•   r„   rÚ   rˆ   r   )rB   r*   re   r   rW   rp   rp   rp   rq   Útest_unrad_fail  s    6&Bÿr±  c                     sú  t dƒ\‰ } }}|ˆ d  | d  }| t|ƒ tt|ƒd d ƒ ˆ t|ƒ t|ƒ tt|ƒd d ƒ i}t||ƒdks~J ‚ttˆ dƒˆ diƒdu sšJ ‚ttˆ dƒˆ diƒdu s¶J ‚ttˆ dk dƒˆ diƒdu sÖJ ‚ttˆ dk dƒˆ diƒdu söJ ‚ttˆ dk dƒˆ diƒdu sJ ‚ttˆ dk dƒˆ diƒdu s:J ‚ttˆ d ˆ d d ƒˆ diƒdu sdJ ‚tˆ d ˆ d d gˆ dƒdu sŠJ ‚tˆ d ˆ d d gˆ dƒdu s°J ‚ttˆ d d ƒˆ dƒdu sÒJ ‚tt‡ fdd„ƒ tt‡ fd	d„ƒ d S )
Nz
x, y, r, trt   ry   TFr   c                      s
   t ˆ dƒS rZ  ©rM   rp   rØ   rp   rq   rž   !  r”   ztest_checksol.<locals>.<lambda>c                      s   t g ˆ dƒS rZ  r²  rp   rØ   rp   rq   rž   "  r”   )	r   r+   r4   rM   r   r   r>   r[   ra  )rf   rÉ   rh   r   Zdict_var_solnrp   rØ   rq   Útest_checksol  s$    &ÿ  ""*&&"r³  c                   C   s¢   t td ƒdtfksJ ‚t dƒdks(J ‚t tdt ƒd tƒdtdƒ tfksRJ ‚t tdt tt  ƒd tƒtd tdƒ tfksˆJ ‚t ttƒtdfksžJ ‚d S )Nrt   )rt   r   ry   rv   r   )rK   re   r#   r$   r]   rp   rp   rp   rq   Útest__invert%  s
    *6r´  c                   C   sž   t t t dt ttƒ  tƒttd ƒgks2J ‚t tt ƒg ksFJ ‚t tt d ƒtttdƒƒƒgkslJ ‚t td td  td td   ƒdgksšJ ‚d S )Nrt   rv   r„   )rB   r]   re   r$   r#   r"   rp   rp   rp   rq   Útest_issue_4463-  s    2&rµ  c                  C   s:  t dƒ\} }}}}}}}}}	}
}}}}}}}| |||||
|f}|||  ||  |d| d|  d|   ||  ||  |d| d|  d|	   ||  ||  |d| d|  d|   ||  |
|  |
d| d|  d|   ||  ||  |d| d|   |
|  g}tt||ddddƒdks6J ‚d S )Nza:rry   TF)r…  r¿   r›   )r   rÒ   rB   )r]   r^   r_   r`   ra   r|   r}   rc   rÑ   Újrb   Úlrj   rn   rå   rd   ri   rÉ   rE  r’   rp   rp   rq   Útest_issue_5114_solvers3  s    ,****ûr¸  c                     s  t dƒ\} }}}}}t dƒ\}}}}	}
}| | | || | || | |  | | d|  d|  d|  d|  |d  d | |	 | | d| d|  d|  |
 |d|  d|  | f	}| || |d| d|  d	|  d
|  d ||| |	|| || d d| d  |d  |||
d| d|  d|  ig‰ | ||
|||||	f}t|g|¢R ddddœŽˆ kstJ ‚t|g|¢R dddœŽˆ d ksšJ ‚t|g|¢R ddiŽg ksºJ ‚t|g|¢R Ž g ksÔJ ‚‡ 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   rœ   rR  rÚ   r„   r‹   ró   TF)r…  r¿   rx   ©r…  r¿   r   r…  c                    s   g | ]}|  ˆ d  ¡‘qS ©r   )rÄ   )rŽ   Úeirw  rp   rq   ræ   i  s   ÿÿz#test_issue_5849.<locals>.<listcomp>©r   rB   )ÚI1ÚI2ÚI3ÚI4ÚI5ÚI6ÚdI1ÚdI4ÚdQ2ÚdQ4ÚQ2ÚQ4ra   Úvrp   rw  rq   Útest_issue_5849C  s<    


*÷$ù	$& 
ÿÿrÌ  c                  C   sä   t dƒ\} }}}}}t dƒ\}}}}	}
}| | | || | || | |  | | d|  d|  d|  d|  |d  d | |	 | | d| d|  d|  |
 |d|  d|  | f	}t|| ||
|||||	ƒ	g ksàJ ‚dS )a  Same as test_issue_5849 but solved with the matrix solver.

    A solution only exists if I3 == I6 which is not generically true,
    but `solve` does not return conditions under which the solution is
    valid, only a solution that is canonical and consistent with the input.
    r¹  rº  rz   rt   rv   rœ   Nr¾  )r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  ra   rp   rp   rq   Útest_issue_5849_matrixm  s    



*÷rÍ  c            
      C   s¤  t dƒ \} }}}}}}}| |  | d| d  d| d  d| d  d|  d  | | d| d  |d  | | |d  | d| d	 d| d	  d|  d	  | | |d  d
| d  |  | | | |d	  | d  d| d |d  |  d| d d|  d|  d  | g	}| d|d|d|d|d|di| d|| |d|tdƒd |d|di| d| |d|||d|tdƒd	 |dig}	t||dd|	ks J ‚d S )Nza, b, c, d, f, g, kru   r‹   rt   r0  r„   rv   r  r)  rÀ   r   rz   Trw   )r   r   rB   )
r]   r^   r_   r`   r|   r}   rb   ZunknownsZ	equationsZanswerrp   rp   rq   Útest_issue_21882ˆ  s     <" ÷$&ýrÎ  c                     s,  t tdƒ\‰ } }tdƒ}tˆ tƒtƒ}t| |ƒ|ƒ}tˆ tƒˆ tƒ t¡ ˆ tƒƒ| gks`J ‚tˆ tƒd ˆ tƒƒdgks€J ‚tˆ tƒdˆ tƒ t¡  ˆ tƒƒd| gks²J ‚tˆ tƒdˆ tƒ t¡  gˆ tƒƒˆ tƒd| iksìJ ‚tˆ tƒdˆ tƒ t¡  ˆ tƒd t d gˆ tƒtƒˆ tƒd| td|d  d igksNJ ‚tˆ |ƒd  | |ƒd  ˆ |ƒd ||ƒd   | |ƒ |¡ ||ƒ| |ƒdd| |ƒgt||ƒd ˆ |ƒd  | ƒ ˆ |ƒ ft||ƒd ˆ |ƒd  | ƒˆ |ƒ fhfksJ ‚ˆ tƒ td¡ˆ tƒ| tƒ  | tƒd  d ˆ tƒ| tƒg}t	t|Ž ƒtdƒ tdƒftdƒtdƒ fhks|J ‚ˆ tƒd | tƒ dˆ tƒ t¡  | tƒd d g}t|ˆ tƒ| tƒddˆ tƒ| tƒgtd| d ƒ t
dƒftd| d ƒt
dƒftd| d ƒ t
dƒ ftd| d ƒt
dƒ fhfksDJ ‚tt‡ fd	d
„ƒ tˆ tƒˆ tƒ t¡ tgdˆ tƒtˆ tƒtƒ dfks–J ‚tˆ tƒttttfƒ tgdˆ tƒttttfƒ dfksÖJ ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ dfksJ ‚tˆ tƒttttfƒ t tgdtˆ tƒ ttttfƒ fksdJ ‚ttˆ tƒ|  ˆ tƒd |  tgdtd| fks J ‚tttdt tƒ ƒtdfksÄJ ‚tttttƒ tgdtdfksêJ ‚tttttƒ d tgdtdtd  fksJ ‚t	ttttƒd  ttƒƒƒtt ƒ tt ƒhksVJ ‚ttttƒ tddttƒ gks~J ‚tttƒttƒ tddg ks¢J ‚ttttƒ tddttƒgksÈJ ‚ttd t d tddtd  d gksøJ ‚ttd t d td ddt d gks(J ‚d S )NZfghr]   rv   rt   r„   r0  Tr    c                      s$   t ˆ tƒˆ tƒ t¡ ˆ tƒgdS )Nrq  )rC   re   r   rp   rX  rp   rq   rž   Å  r”   z!test_issue_5901.<locals>.<lambda>rq  ry   rz   r   r–   )r{   r   r   r   re   rB   r   rf   r+   r˜   r   r[   ra  rC   r9   r#   r1   r3   )r}   rc   r]   ÚDÚGr¦   r’   rp   rX  rq   Útest_issue_5901¡  s¦    ÿÿ"ÿ$ÿ8 ÿ
@ÿ*(þþ
>
"ÿ
6üÿ
ÿÿ
ÿ
"ÿ
"ÿ
(
ÿ
ÿ
ÿ
ÿ
ÿ

ÿ
$ÿ
ÿ

ÿrÑ  c                  C   sº   t ttd t d ddƒtjtdƒd  tdƒ d tj hksFJ ‚ttd t d dd} t| ƒdkr|tdd	„ | D ƒƒs€J ‚ttd t d ƒ} t| ƒdkr²td
d	„ | D ƒƒs¶J ‚d S )Nrt   çš™™™™™¹?TrŠ  r/  rˆ   Fc                 s   s   | ]}|j V  qd S rŒ   ©Z	is_NumberrU  rp   rp   rq   r“   è  r”   z"test_issue_5912.<locals>.<genexpr>c                 s   s   | ]}|j V  qd S rŒ   rÓ  rU  rp   rp   rq   r“   ê  r”   )r˜   rB   re   r   r¬   r+   rÒ   r¡   rw  rp   rp   rq   Útest_issue_5912ä  s    $ÿ"rÔ  c                  C   s”  dd„ } t td ddd js"J ‚t td ddd js<J ‚t ttj ddd jsXJ ‚t td d dd jsrJ ‚t ttj d dd jsŽJ ‚| tdd	t  ƒd
dt  ƒs°J ‚ttt	fD ]D}t|dd	t  gƒƒ}t
|ƒ|u rú| t|ƒd d
dt  ƒsºJ ‚qºttd	t dd	t  giƒ ¡ ƒd \}}| |d	t ƒrR| |d d
dt  ƒsVJ ‚| ttd	t ƒƒtdt ƒƒszJ ‚| tdtd	  ƒdtd	  ƒsžJ ‚| tdtd	  dddtd  ƒsÆJ ‚| ttd	t ƒƒtdt ƒƒsêJ ‚| ttd ƒtd ƒsJ ‚| ttd d	t  ttddƒƒ d ƒtd dt  d ƒsHJ ‚dt t t }t dt | d dt | d t| d fƒg ksJ ‚d S )Nc                 S   s   t |  t¡ƒt | t¡ƒkS rŒ   )rÒ   r”  r   ©Úe1Úe2rp   rp   rq   Útestî  s    z!test_float_handling.<locals>.testr^  TrŠ  r   Fry   rt   ç      ð?g       @rv   g      @rÂ   r„   g!ÌÈ,‹ÿ?éd   gffffffæ?g333333ã?gš™™™™™É?g333333Ó?rÒ  )rB   re   Zis_RationalZis_Floatr   r¬   rD   r£   r¢   r˜   ÚtypeÚitemsr1   r#   r   r_   rg   rh   )rØ  Zcontainr‘   rb   rË  Ztotrp   rp   rq   Útest_float_handlingí  s,    ",*,$$($&ÿ
rÝ  c                  C   s*   t ddd} t| d d ƒdgks&J ‚d S )Nre   Try  rt   ry   r¾  rØ   rp   rp   rq   Útest_check_assumptions  s    rÞ  c                   C   sì   t ttd ƒttd ƒ d ƒg ks(J ‚t ttd ƒttd ƒ d ƒtt tddƒ t t d tt d tt tddƒ gks†J ‚t ttd ƒttd ƒ d d ƒtt tddƒ t t d tt d tt tddƒ gksèJ ‚d S )Nrv   ry   rŠ   r„   rt   )rB   r(   re   r   r   r   rp   rp   rp   rq   Útest_issue_6056  s    (8ÿ"8ÿrß  c                  C   sV   t  ttttt ƒƒƒttt ƒƒ ƒ } t| t dƒdu s:J ‚t| t dddd u sRJ ‚d S )Nrt   TF)Z	numerical)re   r#   r"   r$   rM   rV  rp   rp   rq   Útest_issue_5673  s    &rà  c            
      C   s¸  t dƒ\} }}}}}}}t ddd}|| | |d| | d|     |d| d|   ||  || | || | d|     ||   | | g}	t|	|| |  d||||  | d d	  ||  |  |||d	| |||  |   |||  | | d
|  |||  |   i|d|d|d|digks.J ‚t|	|||gd||||d	 |d	  t|d|  ||  ƒd	  | |d
|  t|d	 d| |  d|d	   ƒ d	| | |  ||||  | i||||d	 |d	  t|d|  ||  ƒd	  | |d
|  t|d	 d| |  d|d	   ƒ d	| | |  ||||  | ig||||d	 ||  |d	  |d	|   |||| d	  ||d	|    | ||| |d	|    igfv s´J ‚d S )Nz$R, C, Ri, Vout, V1, Vminus, Vplus, sÚRfTry  rz   ry   r•   rp  rt   rv   r   ru   r‹   ©r   rB   r+   )
rk   rl  ZRiZVoutZV1ZVminusZVplusrÈ   rá  r’   rp   rp   rq   Útest_exclude  sL    ÿ"(ý$(üüú,@ü,@üû$ üörã  c                  C   sV   t d dt d   dt d   tddƒ } tt| ƒƒtt| d dd ¡ ƒksRJ ‚d S )Nru   r„   rv   rt   rÁ   ZZZ)Údomain)re   r   r˜   rB   r>   Z	all_rootsr—  rp   rp   rq   Útest_high_order_rootsB  s    *rå  c                  C   sÌ   dd„ } | t tt t tt t t gdddƒdks:J ‚| t tt t tt t t gdddƒdkslJ ‚| t tt t tt t gdddƒdksšJ ‚| t tt t tt t gdddƒdksÈJ ‚d S )	Nc                 S   s   t dd„ |  ¡ D ƒƒS )Nc                 S   s   g | ]}|d kr|‘qS r¼  rp   )rŽ   re   rp   rp   rq   ræ   I  r”   z>test_minsolve_linear_system.<locals>.count.<locals>.<listcomp>)rÒ   Úvalues)Zdicrp   rp   rq   ÚcountH  s    z*test_minsolve_linear_system.<locals>.countT)Z
particularZquickrv   Fry   rt   )rB   re   rf   rg   r]   rh   )rç  rp   rp   rq   Útest_minsolve_linear_systemG  s    (ÿ(ÿ.rè  c                  C   s4   t ddd} tt| d | d  d ƒƒdks0J ‚d S )Nre   Trã   ru   rv   ry   )r   rÒ   rB   rØ   rp   rp   rq   Útest_real_rootsR  s    ré  c                  C   sl   dt d  dt   dtd   d dt d  dt  t  dtd   d	 g} tt| tt d
dƒdkshJ ‚d S )NicË†rt   iQÖAiTâkl   1ö'	 iýûa5iPQRiçäžl    d(	 Fr¾   r„   )re   rf   rÒ   rB   )r’   rp   rp   rq   Útest_issue_6528X  s    "&þrê  c                  C   s’   t ddd} td|  d ƒd tdd|   ƒd	 g}t|| ƒtjfgksLJ ‚t|| dd
tjfgkshJ ‚t|| dddtjftdƒfgksŽJ ‚d S )Nre   Trã   r„   rÁ   ru   rv   rÚ   ry   ©r…  Fr»  )r   r   rB   r   r¬   )re   r’   rp   rp   rq   Útest_overdetermineda  s
    (rì  c                  C   sÀ   t dƒ} td| d  d| d   ƒddt t tdƒ gks@J ‚t ddd} td| d  d| d   ƒdgksrJ ‚td	ƒttdƒƒ ttdƒƒ }td| d  dd|    ƒ| |gks¼J ‚d S )
Nre   r„   rt   rv   r   Trã   ru   r‹   )r   rB   r   r   r$   r+   )re   r^   rp   rp   rq   Útest_issue_6605i  s    8& rí  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__ispows  s    rî  c               	   C   sä   t tt d t dt  tj d  ƒ t td  d t dtd  dtd   dt  d ƒd  tddƒ d td d t t dtd  dtd   dt  d ƒd  tddƒ d  ƒ } t| tddd}t|ƒdksàJ ‚d S )Nrt   r„   rÚ   ry   Fr¦  ru   )r+   rj   ri   r   r¬   r   rB   rÒ   ©r   rÓ   rp   rp   rq   Útest_issue_6644y  s*    8"ÿÿÿÿ"ÿÿÿÿÿrð  c                   C   sd   t td t tt gttgƒddgks*J ‚t td tt  tt gttgƒdt t fgks`J ‚d S )Nrt   )r•   r•   rr  )rB   r]   r^   r_   rp   rp   rp   rq   Útest_issue_6752  s    *rñ  c                   C   s¶   t ttd d  td  td t d  ƒdddttd t d dƒttd t d dƒttd t d dƒttd t d dƒttd t d dƒttd t d dƒg	ks²J ‚d S )	Nry   rt   r‹   r•   r   rv   r„   ru   )rB   re   rW   rp   rp   rp   rq   Útest_issue_6792†  s
    *.((ýrò  c                     s  t ddd\‰ } ttˆ d ƒdtˆ d ƒ  ƒddgks<J ‚ttˆ ƒd tˆ ƒt gˆ ƒdgksdJ ‚tttˆ d	 ƒd
 ƒƒtj tdƒhksJ ‚ttt	ˆ d ƒt	ˆ d d	 ƒ dƒˆ ƒt
ddƒtdƒd  tdƒ d tj gksæJ ‚tdtˆ ƒ tˆ d ƒ ƒdt
ddƒgksJ ‚t 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sdJ ‚ttˆ ƒd tˆ ƒd  ƒd }t|ƒt|ˆ ƒksœJ ‚t ddd}tt|ƒd ƒdt dt gksÎJ ‚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sxJ ‚t ddd\‰ } tˆ | t  d dt  ƒˆ dt | dt iks¾J ‚t ddd‰ tˆ |  d dt  ƒˆ d| dt iksøJ ‚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sXJ ‚t dƒ‰ tdˆ  dˆ   ƒtt tdƒ gksŒJ ‚d S )Núx yTrã   rv   rt   ry   r0  )rz   rÁ   rÚ   rl   r•   r
  r#  re   rÑ   ©Z	imaginaryrŠ   c                      s   t tˆ ƒd ƒS r[  )rB   Úabsrp   rØ   rp   rq   rž   ¥  r”   z6test_issues_6819_6820_6821_6248_8692.<locals>.<lambda>rn  )r}  r„   r   rz   r|   )r   rB   rõ  r   r   r˜   r   rª   r   r   r   r+   r¬   r!   r    r   r[   r€   r   r$   )rf   r   rÑ   rn  r|   rp   rØ   rq   Ú$test_issues_6819_6820_6821_6248_8692  s>    ,(,&&ÿ
0ÿ &:&6.,,rö  c                  C   s4  t dƒ\} }}}}}| d | | | |  | |  d ||  | |   }t dddd\}}}	|dd||    |	|    }
||
  ¡ }|t|ƒ ¡ 9 }t|| ƒ}| ¡ }|||	g}t||dd} t| ƒdksÐJ ‚|||  |||   ||| |	|| ||  i}|D ](}| d |  ¡ ||  ¡ ksJ ‚qd S )	Nzs, tau_c, tau_1, tau_2, phi, Krt   ry   zK_C, tau_I, tau_DT)rz  Znonzerorw   r   )r   Ztogetherr@   r›   r>   ZcoeffsrB   rÒ   )rÈ   Ztau_cZtau_1Ztau_2ÚphiÚKÚtargetZK_CZtau_IZtau_DZPIDr   r_   ÚvarsZknownsolutionÚvarrp   rp   rq   Útest_issue_14607¾  s*    ÿ6ÿ

þrü  c                     sj  ddl m‰ m‰ ttˆ dˆ   tˆ ƒ ˆ ƒˆ ƒˆ tˆ ƒhksBJ ‚tˆ ˆ ƒg ksTJ ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   ¡ƒt
dtj ƒd gks˜J ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   d d ¡ƒt
dttdƒ ƒ ƒd t
dttdƒƒ ƒd gksJ ‚tˆ d dˆ   d  ˆ t	ˆ ƒdˆ   ¡ƒt
dtdtdƒ ƒ ƒd t
dtdtdƒ ƒ ƒd gksnJ ‚ˆ tˆ ƒ d  ˆ ˆ tˆ ƒ ¡} t| ƒt
dtt
dƒ ƒ ƒgks´J ‚tt‡ ‡fdd„ƒ ddt
t	dƒ d ƒ t	dƒ g}tˆ d dˆ   ˆ ƒ|ks
J ‚ttdt	ˆ ƒ ˆ t	dƒ  ƒƒt|ƒks8J ‚tt
dˆ  ƒˆ ˆ ƒˆtˆƒ d gksfJ ‚d S )	Nr   ©re   rf   ry   rt   rv   c                      s   t ˆ tˆ ƒtˆˆ  ƒ  ˆ ƒS rŒ   )rB   r3   r$   rp   rý  rp   rq   rž   ç  r”   z+test_lambert_multivariate.<locals>.<lambda>rŠ   )r_  re   rf   rH   r>   r#   rJ   rB   rÄ   r$   r"   r   r{  r+   r[   r€   r˜   )r   r‘   rp   rý  rq   Útest_lambert_multivariateÛ  s"    2D20ÿ
*6ÿ
 &" .rþ  c                   C   sn   t dttƒ ttdƒ  tƒdgks(J ‚tt tt tt  ƒtƒtt tttƒ t ƒ ttƒ hksjJ ‚d S r[  )rB   r3   re   r˜   r]   r"   r$   rp   rp   rp   rq   Útest_other_lambertî  s    ( ÿrÿ  c            
   	   C   s  t td t ttd t ƒ d ƒtddƒtddtdƒ  ƒd  tddƒtddtdƒ  ƒd  gkslJ ‚t td t ttd t d ƒ d ƒtddƒtddtdƒ  ƒd  tddƒtddtdƒ  ƒd  gksÜJ ‚t tt ttd ƒ tƒdtt d ƒ gksJ ‚t tt ttd ƒ  t¡tƒdttdƒ ttƒ d ƒ dttdƒttƒ d ƒ gkspJ ‚t dt ttd ƒ  t¡tƒdttdƒ d ƒ dttdƒd ƒ dttdƒ d dƒ gksÖJ ‚t tttƒ dt  d tƒtdttdƒ ƒ ƒgksJ ‚t td  dt  tƒdddttdƒd ƒ tdƒ gksRJ ‚t td dt  tƒdddttdƒd ƒ tdƒ gksJ ‚t dt d dd	t d   tƒ} t	| ƒdkr| d
  
¡ td	dƒtdtddƒ tdƒ d ƒdtdƒ   ksJ ‚t dt d dtddt  ƒ  tƒtddƒtdttddƒƒ d ƒd  gks\J ‚t ttƒt  ttd d ¡ƒt ttdƒ d ƒ tdtdƒ ƒgksªJ ‚tdt d  }t dt|ƒ tt|ƒ  | tƒ} dttƒ }tdƒt }td }|td| ƒ td  }|tddƒ d }| |t|| d  ƒ |t||d  ƒ |t|ƒ d gkshJ ‚ttddƒƒ}td	 }dtddƒ  }dtddƒ t }|tddƒ |tddƒ  d }t dt|ƒ | tƒ} | |td| | ƒ d |t|||  ƒ |t|||  ƒ gksJ ‚tddd}ddd| d   d|  d }	t|	|tt|	ƒ|ƒƒtddƒtdtdƒ ƒdtdƒ   gksŽJ ‚tt dttƒ ttƒd  ƒƒtdƒtdttdƒ d ƒ tdƒ ƒhksÞJ ‚t dttƒ dttƒ  ttttƒ ttƒ ƒ tƒtt tdtd  tdt ƒ ƒd  ƒt gksJJ ‚t tt ttd ƒ  td¡tƒ} t tddƒ }tdƒt }|d }| dt|d ƒ dt|| d  ƒ dt||d  ƒ gksÒJ ‚t dt ttd ƒ  td¡tƒdttddƒƒ dttddƒtdƒt d  ƒ dttddƒtdƒt d  ƒ dttddƒdƒ gks`J ‚t td td ttƒ  ttddtdtt d ƒ itdttd ƒ igks´J ‚t td td  td  tƒttdtdƒ d dttƒ d  tt tddƒ  ƒƒgksJ ‚d S )Nrt   ry   r•   r„   rv   rŠ   rz   ru   éûÿÿÿr   i ØÿÿrÁ   iëÿÿÿr‹   rd   Try  rR  rw   )rB   re   r#   r   r+   r"   r]   r   r$   rÒ   r`  r*   rÄ   r   r^   r   rI   rH   r>   r˜   r1   r-   rg   rf   r   )
r‘   Úaxrí   rî   rF  rG  rH  rI  rd   r   rp   rp   rq   Útest_lambert_bivariateõ  s®    "  þ
&  þ
48ÿ
þÿ
ÿ
@>"2ÿ
$(ÿ
$ÿ"ý ý $ÿ&ÿ4,ÿ"ý 02ÿÿ
"(ÿ
8ÿr  c                   C   s’  t ttƒttƒ ƒdt tdt gks*J ‚t ttƒttƒ ƒdttddƒtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒtdtdƒt	  ƒ d  tdƒt	 d  ƒ dtt
jtdƒt	 d  tdƒtdtdƒt	  ƒ d  ƒ gks<J ‚t ttƒttƒ ƒdt	t gksbJ ‚t dttƒ ttƒ tƒtt
jƒgksŽJ ‚d S )Nr   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_trigD  s     *@Dÿÿÿÿý&r  c                  C   sø   ddl m}  tttƒ| tƒ ƒdttddƒtdƒd  tdtdƒ d ƒd  ƒ dttddƒtdƒd  tdtdƒ d ƒd  ƒ dttdƒ d tj	 tddtdƒ  ƒd  ƒ dttddtdƒ  ƒ d tdƒd  tj	 ƒ gksôJ ‚d S )Nr   ©Úsechrt   r•   ru   rz   )
Ú%sympy.functions.elementary.hyperbolicr  rB   r'   re   r%   r   r+   r   r¬   r  rp   rp   rq   Útest_rewrite_trighQ  s    4422ür  c                  C   s”  t ttƒ tttdtd td     ƒ } t| tddttttt ƒ  ƒ ttttt ƒ  ƒgkshJ ‚tttd ƒtddt  ƒ d ƒdtdtdƒ ƒttddƒƒ d  tdƒd  tdtdƒ ƒ ttddƒƒ d d tdƒd  gdtd	tdƒ d
 d  ƒd  tdƒd  dtd	tdƒ d
 d  ƒd  tdƒd  gfv sTJ ‚tttdt ƒd ƒtttƒ d ƒ tdƒ ƒg ksJ ‚d S )Nr•   rt   T)Úforcerv   ry   rŠ   iôÿÿÿiÜÿÿÿr‹   )	rg   r$   re   rf   rB   r+   r#   r   r(   rV  rp   rp   rq   Útest_uselogcombine\  s    ,<"02ÿ,,ÿýr	  c                   C   s.   t ttdƒtd  tƒdtdƒ gks*J ‚d S r\  )rB   r0   re   r   r+   rp   rp   rp   rq   Ú
test_atan2h  s    r
  c                   C   s„   t ttƒt tƒttƒgks J ‚t ttƒt tƒttƒgks@J ‚t ttƒt tƒttƒgks`J ‚t ttƒt tƒttƒgks€J ‚d S rŒ   )rB   r5   re   rf   r8   r6   r7   rp   rp   rp   rq   Útest_errorinversesl  s       r  c               	   C   sT  t dƒ} tdƒ|  td| d  ƒ | d tdƒtd| d  ƒ d   }t|| ddd }|tddƒtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ   ddtddƒtdƒt d  td	d
ƒtdƒt d  tddƒ     ftddƒddtd	d
ƒtdƒt d  tddƒ    td	d
ƒtdƒt d  tddƒ  fhksPJ ‚d S )Nrk   rt   ry   Tr    ru   rv   r•   éû   r¸   éo   r0  r÷   )r   r+   rB   r   r   )rk   r   rÓ   rp   rp   rq   Útest_issue_2725s  s,    @*ÿÿ$ÿÿÿÿÿ"ÿþr  c                  C   sh  t dƒ\} }}}}}}}}}	}
}}}}}}t| ||  ||  g|d| d|  d|   ||  ||  g| | |d| d|  d|    ||  g| | |d| d|
  d|    |	|  g| | |	d| d|  d|    ||  g|	 | |d| d|    ggƒ}t|||	|| |gƒ}tt|ƒt|ƒdd}tdd„ | ¡ D ƒƒdksdJ ‚d S )Nzb:rry   Frš   c                 S   s   g | ]}|  ¡ ‘qS rp   )Ú	count_ops)rŽ   rÈ   rp   rp   rq   ræ   ‹  r”   z(test_issue_5114_6611.<locals>.<listcomp>iÆ  )r   r<   rB   r£   rè   ræ  )r^   r_   r`   ra   r|   r}   rc   rÑ   r¶  rb   r·  rj   rn   rå   rd   ri   rÉ   r’   rË  r‘   rp   rp   rq   Útest_issue_5114_6611}  s    *@\Lýr  c                  C   sž   t ddtdƒƒ} |  ¡ t| ƒks$J ‚d| d< |  ¡ t| ƒks@J ‚t ddttdƒƒƒ} |  ¡ t| ƒkshJ ‚tdddƒ}t|ƒt|ƒ  kr”| ¡ ksšn J ‚d S )Nrv   za:9ry   rr  r0  rt   )ry   rt   ry   r„   )	r<   r   ZdetrP   r£   rê   r=   rQ   rR   )rj   rÈ   rp   rp   rq   Útest_det_quickŽ  s    r  c                  C   s’   t ddd\} }tt| d |d  ƒd | ƒt|d  d ƒ t|d  d ƒgksXJ ‚t ddd\} }tt| d |d  ƒd | ƒg ksŽJ ‚d S )Nza bTrã   rt   rv   r0  rô  râ  rQ  rp   rp   rq   Útest_real_imag_splittingš  s    $ÿr  c                  C   sB   dt d  dt d   dt   d } tdd„ t| ƒD ƒƒs>J ‚d S )Nrz   rv   r„   rt   ru   c                 s   s   | ]}t t |¡ƒV  qd S rŒ   )r   r   rä   rÐ   rp   rp   rq   r“   ¤  r”   z"test_issue_7110.<locals>.<genexpr>)re   r«  rB   rÍ   rp   rp   rq   Útest_issue_7110¢  s    $r  c                   C   s*   t dt ddt   ƒdt gks&J ‚d S rW  )rB   re   rU   rp   rp   rp   rq   Ú
test_units§  s    r  c                  C   s¢   t dƒ\} }}td|d  | |d  |  | dƒ}t|d|d  ƒ}t| d| |d  ƒ}ttt|||ƒ| ||gdƒƒ}t|ƒttd	gd
gdggƒƒksžJ ‚d S )NzA,B,Vg®Gáz²ƒ@g     €C@rô   r   g    d6 Ag    0Œ!A)r   r   r   z4442890172.68209z4289299466.1432z70.5389666628177)r   r   r<   rA   r   rb  )rj  rk  ÚVÚeq1Úeq2Úeq3rÓ   rp   rp   rq   Útest_issue_7547«  s    &
þÿr  c                  C   s*   t ddd} tt| ƒd ƒdgks&J ‚d S )NrÉ   Trã   rt   r„   râ  )rÉ   rp   rp   rq   Útest_issue_7895·  s    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sJ ‚t||| |  f| |fƒg ks²J ‚|d
7 }t||f| |fƒg ksÔJ ‚t||f| |fdd|ksòJ ‚d S )Nró  Trã   rt   rˆ   rv   é¿   rÀ   i‡  r‹   Fr¾   )r   r+   r   rB   )re   rf   rÖ  r×  r]   r^   r‘   rp   rp   rq   Útest_issue_2777¼  s    8"r  c                  C   s"   d} t t|  tƒd | ksJ ‚d S )Ng{[Rs±Ò8r   r¶   )Únumberrp   rp   rq   Útest_issue_7322Ê  s    r  c                   C   s.   t tdd„ ƒ t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s   t tdddS )N)r•   ry   Úbisect)Úmethod)rA   re   rp   rp   rp   rq   rž   Ð  r”   ztest_nsolve.<locals>.<lambda>c                   S   s(   t tt d tt tt ftttfdƒS )Nrv   )iÎÿÿÿrõ   )rA   re   rf   rg   rp   rp   rp   rq   rž   Ñ  r”   c                   S   s   t tt tt fdƒS )Nro  )rA   re   rf   rp   rp   rp   rq   rž   Ò  r”   )r[   ra  r   rp   rp   rp   rq   Útest_nsolveÏ  s    r!  c                      sæ   t tttd  t d tƒƒdks&J ‚t tttd  t d tƒƒdksLJ ‚tttd  t d tƒg ksnJ ‚ttdd„ ƒ td t d ‰ tˆ ddˆ    ƒ‡ fdd„tdƒD ƒksºJ ‚td ‰ tˆ d	dˆ    ƒtjgksâJ ‚d S )
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   rž   Ú  s    z.test_high_order_multivariate.<locals>.<lambda>c                    s   g | ]}t ˆ d  |ƒ‘qS rD  rV   rÐ   ©r`   rp   rq   ræ   à  r”   z0test_high_order_multivariate.<locals>.<listcomp>rt   )	rÒ   rB   r]   re   r[   r€   rê   r   r¬   rp   rp   r#  rq   Útest_high_order_multivariateÕ  s    &&".r$  c                   C   sX   t dt d ƒdgksJ ‚t dtd  d ƒdgks8J ‚t tdddƒddgksTJ ‚d S )Nr   ry   rt   zx*(1/x**0 - x)F©Úevaluate)rB   re   r   rp   rp   rp   rq   Útest_base_0_exp_0å  s
    ÿr'  c                   C   sd   t dtd  tgƒtƒ ksJ ‚t dtt  tgƒtt hks@J ‚t dttdƒ tgƒthks`J ‚d S )Nry   r   rv   )rS   re   r˜   rf   r*   rp   rp   rp   rq   Útest__simple_densì  s    "r(  c                   C   s”   t tttƒt td  d tƒƒdks*J ‚t tdtd  dtd tddƒ  td   dtd tddƒ  t  dt  d td	d
ƒdksJ ‚d S )Nrv   ry   r   r¡  rt   r¢  r˜  r£  Fr¤  )rÒ   rB   r+   rf   re   r   rp   rp   rp   rq   Útest_issue_8755ò  s    *,ÿÿÿÿÿr)  c                  C   sP  d} d}d}d}d}d}d}d}t ttf}t |  d	 t| d	  |t d	  }	|t  d	 |t d	  td	  }
t | d	 t| d	  |t d	  }|	|
|f}tt |  d	 t| d	  ƒt | }|
}tt | d	 t| d	  ƒt | }|||f}t||ƒ}t||ƒ}t||d
d}dd„ |||fD ƒ\}}}||  krF|ksLn J ‚d S )Nr   i”ýÿÿi˜  é~   rž  r7  éÍ   éh   rt   Trë  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   rÐ   rp   rp   rq   r“     r”   z7test_issue_8828.<locals>.<listcomp>.<setcomp>.<genexpr>)r¢   )rŽ   r¶  rp   rp   rq   Ú	<setcomp>  r”   z-test_issue_8828.<locals>.<listcomp>.<setcomp>rp   )rŽ   rk   rp   rp   rq   ræ     r”   z#test_issue_8828.<locals>.<listcomp>)re   rf   rg   r+   rB   )rî   Úy1Zr1rF  Úy2rG  Zy3Zr3rË  Úf1Úf2Zf3rf  Zg1Zg2Zg3rÐ  rj  rk  rl  rd   ri   rÉ   rp   rp   rq   Útest_issue_8828û  s,    
$ $
$$


r2  c                   C   sþ  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s¢J ‚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súJ ‚d S )Nrv   r‹   r   r   rR  rz   r0  rt   r„   rC  ru   r   r•   ry   r)  )rB   r3   re   r   r   r   r$   r1   rp   rp   rp   rq   Útest_issue_2840_8155  s    *,,*4((&&÷
.ÿr3  c                   C   s"   t ddtd   ƒdgksJ ‚d S r  r¶   rp   rp   rp   rq   Útest_issue_9567)  s    r4  c                  C   s€  t tt ƒt gksJ ‚t td t ƒt ttƒ tttƒ gksFJ ‚t td dt  ƒtdt ƒ tdƒttƒ d tdƒtdƒ t ttƒ d  tdƒttƒ d tdƒtdƒ t ttƒ d  gksÒJ ‚t td tt gttƒtdtt iksüJ ‚t td d tt gttƒdt t fdt t fgks:J ‚ttd  d } tt d dt  }tt | |gttƒƒdks|J ‚d S )Nrt   rv   r„   rR  rz   )rB   re   r   r   r+   r)   rf   rÒ   rÕ  rp   rp   rq   Útest_issue_11538-  s    .22ý
*ÿr5  c            	      C   s  t dƒ\} }}}}}}d| |  ||  d| |  ||  d||  ||  || d  |d  ||d  |d  ||d  |d  g}t|| ||||||gdd}|| t|d  d ƒ |t|d  d ƒ |t|d  d ƒ |||||di| t|d  d ƒ|t|d  d ƒ|t|d  d ƒ|||||di| tdƒ | d t|d  d ƒd  |tdƒ| d t|d  d ƒd  |t|d  d ƒ|| d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |di| tdƒ | d t|d  d ƒd  |tdƒ| d t|d  d ƒd  |t|d  d ƒ || d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |di| tdƒ| d t|d  d ƒd  |tdƒ | d t|d  d ƒd  |t|d  d ƒ|| d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |di| tdƒ| d t|d  d ƒd  |tdƒ | d t|d  d ƒd  |t|d  d ƒ || d td|d  d	 ƒd  || d tdƒt|d  d ƒ d  |digksJ ‚d S )
Nza,b,c,d,e,f,gry   rt   Trw   r•   rv   rŠ   r‹   râ  )	r]   r^   r_   r`   ra   r|   r}   ZtermsrÈ   rp   rp   rq   Útest_issue_12114=  s@    66ÿ* ÿ$ÿ(8",ý(:",ý&:",ý&<",ýðr6  c                   C   sL   t dtt  ƒg ksJ ‚t tt tƒg ks.J ‚t tt t tƒg ksHJ ‚d S rZ  )rB   r   re   rp   rp   rp   rq   Útest_infY  s    r7  c                     sò   t dƒ‰‡fdd„tdƒD ƒ} tdƒ}tt| |ƒƒ}|d d… |dd …  \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}| d d… | dd …  \‰‰‰‰ t‡ ‡‡‡fdd„tdƒD ƒˆˆˆfƒ}|| d	   |¡ ¡ ||d	   ¡ ksîJ ‚d S )
Nr|   c                    s   g | ]}ˆ |ƒ‘qS rp   rp   rÐ   rX  rp   rq   ræ   a  r”   z$test_issue_12448.<locals>.<listcomp>rl   zx:15rv   c                    sT   g | ]L}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS ©r„   ry   rt   rv   rp   rÐ   ©r_   re   rf   rg   rp   rq   ræ   f  s   ÿc                    sT   g | ]L}ˆ d |  ˆ ˆ d | d  ˆ  ˆ d | d  ˆ  ˆ d | d   ‘qS r8  rp   rÐ   r9  rp   rq   ræ   j  s   ÿr   )r   rê   r   rx   r•  rB   Zxreplacer  )Zfunrˆ  r–  ZssymZsfunrp   )r_   r|   re   rf   rg   rq   Útest_issue_12448_  s&     ÿÿ ÿÿÿr:  c                   C   sî   t td dt  ƒdthks J ‚t td dt  tƒthks@J ‚t td dt  tgƒthksbJ ‚t dt dt  dt  ttgƒtthksJ ‚t dt dt  dt  ttƒtthks¼J ‚t dt dt  dt  tthƒtthksêJ ‚d S )Nrt   ry   )rT   re   rf   rg   rp   rp   rp   rq   Útest_denomsq  s      ".,r;  c               &   C   s:  t dƒ\} }}}}}| d |  | | | | | | | | | | | | | | | | | | |  d |d  d| d  || |d  |d  |d  || |d  |d  |d  || d| d  |d  || | | | | || |d  |d  |d  |  d |d  |d  |d  |d  |d  | d ||  |d  |d  |d  |d  || |d  |d  |d  || | | | | || |d  |d  |d  | d ||  |d  |d  |d  |d  |  d |d  |d  |d  |d  |d  | d |d  ||  |d  | ||  | | | || d| d  |d  || |d  |d  |d  | d |d  ||  |d  |  d d| d  |d  | ||  | | | || | || | | ||  | ||  |  |d  | d g%}| d|tddƒ|tddƒ|tddƒ|tddƒ|di| d|tj|tddƒ|d|d|di| d|tddƒ|tddƒ|tddƒ|tddƒ|di| d|d|d|d|d|di| d|tddƒ|tddƒ|td	ƒd |td	ƒ d |di| d|tddƒ|tddƒ|td	ƒ d |td	ƒd |dig}t|ƒ|ks6J ‚d S )
Nzx0 x1 x2 x3 x4 x5rt   rv   r‹   ry   rz   r•   r   ru   )r   r   r   r¬   r+   rB   )rí   rî   rF  rG  rH  rI  re  Zsolsrp   rp   rq   Útest_issue_12476z  s*    <DLNN20PNR>ö2"288ûr<  c                  C   s:   t dƒ} t| tdƒtdƒ  tdƒ | f| ƒg ks6J ‚d S )Nrh   ru   rt   râ  )rh   rp   rp   rq   Útest_issue_13849‘  s    r=  c                  C   s@   ddl m} m} td| |  t t tƒd|  t gks<J ‚d S )Nr   ©ÚnewtonÚkilorÚ   iÀàÿÿ)Úsympy.physics.unitsr?  r@  rB   re   rf   r>  rp   rp   rq   Útest_issue_14860–  s    rB  c               	   C   sf  t dƒ\} }}}td|  d d |d   | d d |d   d|  d d |d   | d d |d   || d g|| ||ƒdd| td|d d  ƒ |fdd|td|d d  ƒ |fgksÊJ ‚t||| d|d   d | d d|d   d g|||ƒ|dtdƒ d f|dtdƒd fgks4J ‚t||d  d ||d  d fƒg ksbJ ‚d S )Nz:4r•   ry   rt   r   rz   r0  râ  )rb   rc   r]   r^   rp   rp   rq   Útest_issue_14721›  s*    ..ýý þý0ÿÿ"ÿÿ
rC  c                  C   sl   t ddd} tt| d d| d   d ƒt| d d| d   d ƒ d	t| ƒ |   | ƒtdƒgkshJ ‚d S )
Nre   Trã   r„   é‚   rt   iA  i  rù   )r   rB   r+   r   rØ   rp   rp   rq   Útest_issue_14779©  s    0ÿÿÿÿrE  c                  C   sú   t td ttd td ddfƒtdtditdtdigks>J ‚t td tdtd ddfƒtdtdikslJ ‚t td ttd td ddfƒtdtdiksžJ ‚tdt dt  d	 d
t t ƒ} tdt d dt d ƒ}t | |gƒtdtdiksöJ ‚d S )Nrt   rv   Fr%  rŠ   r„   r•   iá0  iÕW i¢éÿÿrz   rÚ   r÷   rœ   r4  )rB   rf   r	   re   r   r   )r  r  rp   rp   rq   Útest_issue_15307¯  s     ÿ
ÿ 
ÿ"rF  c                   C   sÔ   t td tƒdgksJ ‚t td gtƒtdiks4J ‚t ttdtd  d  tdt  ƒtƒg ksdJ ‚t ttdtd  d  tdt  ƒgtƒg ks–J ‚t ttdtd  d  tdt  ƒttdƒgtƒg ksÐJ ‚d S )Nrv   rt   ry   )rB   re   r   rf   rp   rp   rp   rq   Útest_issue_15415»  s
    02rG  c                  C   s  t ttd dt  d td dt  d  dƒƒg d¢ks>J ‚t ttd  d ƒd	gks\J ‚t t t d  d ƒdgks~J ‚t td d
 td d  d ƒd	dgksªJ ‚t td dt  d td d  dddtdƒ    ƒtdƒgksðJ ‚t tttj  dtdƒ  ƒtdƒgksJ ‚t td d t d ƒdgksBJ ‚t tdt  d ƒddgksdJ ‚t td dt  tdƒ ƒddgksŽJ ‚t tttj  tddƒ ƒtddƒgks¼J ‚t ttdƒƒ t d ƒdtdƒtdtddƒ ƒtt	   gksJ ‚t tdƒt ttdƒƒ ƒtjgks,J ‚t tdƒ t dtdƒ  ƒddtdƒd  dt	d   dt t	 tdƒ  tdƒd dt	d    gksœJ ‚t tdƒt dtdƒ  ƒdgksÄJ ‚t tt d ƒdgksàJ ‚t dt t dt  ƒdgksJ ‚t tdƒtdƒ t dtd
ƒ d tddƒ  ƒtddƒgksHJ ‚t
dƒ} t | t | d  tƒdgksrJ ‚t | t d|   tƒdgks”J ‚t | t |  tƒdgks²J ‚t
ddd} t | t | d  tƒdgksàJ ‚t | t d|   tƒdgksJ ‚d S )Nrt   rÁ   rü   r  r—   ry   )rt   rv   r„   ru   r‹   rÁ   r„   rz   r‹   rv   r  rÚ   r0  ru   r^   r•   Try  )rB   r   re   r+   r   r¬   r   r$   r   r   r   )r^   rp   rp   rq   Útest_issue_15731Ã  s4    >",F.$"*.F*Fÿ($D"""rH  c                   C   sJ   t td ttd   tƒsJ ‚t ttd  td  td  d ƒsFJ ‚d S )Nr„   rÒ  rv   rt   rÙ  )rB   re   rf   r   rp   rp   rp   rq   Útest_issue_10933ã  s    rI  c                  C   s,   t ddd} tt| t ƒ| ƒdgks(J ‚d S )Nre   Trã   r   )r   rB   rõ  rf   rØ   rp   rp   rq   Útest_Abs_handlingè  s    rJ  c                  C   s†   t dƒ} td| d  d|   d dk| dkg| ƒtju s<J ‚t| d d| d   d	|  d  d
 dk| d dkg| gƒtju s‚J ‚d S )Nre   rt   ru   rÀ   r   g      ø?rv   g)\Âõ( @g=
×£p=L@éj   ry   )r   rB   r   ÚfalserØ   rp   rp   rq   Útest_issue_7982í  s    4rM  c                  C   sP   t dƒ\} }t| | |  | | | |  | g| |gƒ||d  |fgksLJ ‚d S )Nró  ry   r¾  rý  rp   rp   rq   Útest_issue_14645õ  s    rN  c                  C   sR   t dƒ\} }ttd| dk f| | dkfƒ| ƒ|td| dk f| dfƒigksNJ ‚d S )Nró  rŸ   rÒ  T)r   rB   r,   rý  rp   rp   rq   Útest_issue_12024ú  s     ÿrO  c                   C   s¬   t dt t t tƒtttƒtt  ƒ ttdƒƒ tttƒtt  ƒttdƒƒ gks\J ‚t ttd  td  tƒttdtdƒ dttƒ  dt t  ƒƒgks¨J ‚d S )NrÁ   rü   iõÿÿÿ)rB   re   r   r+   r$   r   r#   r"   rp   rp   rp   rq   Útest_issue_17452 	  s    4ÿ
rP  c                   C   s0   t tttdƒd  ƒt  t tƒg ks,J ‚d S rŽ  )rB   r5   re   r   r   r   rp   rp   rp   rq   Útest_issue_17799	  s    rQ  c                  C   sN   t ddd} ttt| d d ƒ|  ƒ|  ƒddtdƒ dtdƒ gksJJ ‚d S )Nre   Trã   rt   ry   r•   )r   rB   rõ  r+   rØ   rp   rp   rq   Útest_issue_17650
	  s    rR  c                  C   s\   dt d  dt d d tdƒd    ddt d d tdƒd     } t| ƒd u sXJ ‚d S )Niøÿÿÿrt   r0  ry   r„   rv   )re   r   rL   rV  rp   rp   rq   Útest_issue_17882	  s    HrS  c                   C   s„   t tt
 td  ƒtƒg ks J ‚t tt td  ƒtƒg ks@J ‚t tt
 td  ƒtƒg ks`J ‚t tt td  ƒtƒg ks€J ‚d S rY  )rB   r#   re   rp   rp   rp   rq   Útest_issue_17949	  s       rT  c                   C   s  t tttdƒdƒƒddgks J ‚t tttdƒttdƒ tƒƒg d¢ksJJ ‚t tttdƒdƒƒddgksjJ ‚t tttdƒ tƒttdƒ gksJ ‚t tttdƒ ttdƒ ttƒ tƒttƒ ttdƒ ttdƒ gksÚJ ‚t td ttd dƒ tƒg d¢ksJ ‚d S )Nrt   rv   rz   )rR  r   ry   r   ry   )rz   r•   rv   )rB   r   r   re   Úpowr]   rf   r3   rp   rp   rp   rq   Útest_issue_10993	  s     * &JrV  c                  C   sr   t t d } t t }t| |gt tƒt t tdt iks:J ‚t d t }t| |gt tƒt dt tdt iksnJ ‚d S )Nry   r•   rt   rz   )re   rf   r
   rB   r   )r  r  r  rp   rp   rq   Útest_issue_11553$	  s
    &rW  c                  C   sÀ  t dƒd } tttƒd ttƒd  ƒ tdttƒd  dttƒd   ƒtd|  ƒtd|  dtdƒt   d ƒ td|  dtdƒt   d ƒ gksžJ ‚t j}tttƒd ttƒ ƒdt| tdƒd  tdƒtdtdƒ ƒ d  ƒ dt|tdƒd  tdƒtdtdƒ ƒ d  ƒ dttdƒ d | tdƒtdtdƒ ƒ d  ƒ dttdƒ tdtdƒ ƒ d | tdƒd  ƒ gks”J ‚tdttƒ ttƒ ƒtdƒgks¼J ‚d S )Nry   rv   ru   r„   rt   rz   )	r   rB   r1   re   r3   r/   r+   r   r¬   )rh   rc   rp   rp   rq   Útest_issue_19113_19102,	  s    "* þ
4244ürX  c               	   C   sª   t dƒd } t dƒd }tdƒd }tdƒd }tdtd d  d ƒd| |  t| | ƒ | |  t| | ƒ ||  t| | ƒ ||  t| | ƒ gks¦J ‚d S )Nrv   r„   ru   rÚ   ry   rt   )r   r+   rB   re   ©r]   r^   r_   r`   rp   rp   rq   Útest_issue_19509;	  s    ürZ  c               	   C   sò   t dƒ\	} }}}}}}}}|| | |  | }	d|d | d  | dt||	 ƒ   }
||||	t|
ƒ    }dt|| | ||| | |  |   ƒ dt||| | |  |  ƒ  }| |d|   |d|   d g}t||ƒ|ksîJ ‚d S )NzTHT HT DBH dib c0 c1 c2 c3 c4ry   )r   r#   r$   rB   )ZTHTZHTZDBHZdibZc0Zc1Úc2Úc3Zc4r|   Úrhsr   ZtermrÓ   rp   rp   rq   Útest_issue_20747F	  s    (*ÿ"r^  c                  C   s2  t dt  d  } t|  t dt d i¡ t¡dktƒtdƒtk ttdƒd k @ ksVJ ‚t|  t dt d i¡ t¡dktƒtdƒd tk ttdƒd k @ ks J ‚t|  t dt d i¡ t¡dktƒtd	ƒd tk ttdƒk @ ksæJ ‚t|  t dt d i¡ t¡dktƒtdƒtk ttdƒd k @ ks.J ‚d S )
Nry   rt   rv   r   r•   rR  rz   r„   r   )rh   rB   rÄ   re   r   r   rX  rp   rp   rq   Útest_issue_20902P	  s
    FJFr_  c               	   C   sÄ   t ddd} tttdƒƒ ttt| ƒƒ tttƒ g}t|tttƒtttdƒƒttttdƒƒƒttt| ƒƒikstJ ‚t	tƒt	t ƒ ttƒt	tƒt	t ƒ   t d g}t|tƒtdiksÀJ ‚d S )Nr]   Trã   r„   ru   )
r   re   r&   r1   rf   r'   rg   r(   rB   r#   )r]   ru  Z	newsystemrp   rp   rq   Útest_issue_21034X	  s    *(ÿ
6r`  c                  C   sÔ   t ttd t d  td td   td  ƒ t d td   } tt t d td   }t||   t t   ||  ft||   t t   ||  fg}ttd td  td  t t tt  t gttƒ|ksÐJ ‚d S rY  )r]   r+   rk   r^   r_   rB   re   rf   )rg   rh   rÓ   rp   rp   rq   Útest_issue_4886d	  s    @<ra  c                  C   sT   t ddd\} }}}t| |t  ||t   tƒt||  ƒt|| ƒ gksPJ ‚d S )Nri  Try  )r   rB   re   r$   rY  rp   rp   rq   Útest_issue_6819k	  s    rb  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   rØ   rp   rp   rq   Útest_issue_17454p	  s    rc  c                  C   sB   ddt dƒ d  g} tdt t dtd  ƒ d ƒ| ks>J ‚d S )Nr$  rt   )r+   rB   re   )r´   rp   rp   rq   Útest_issue_21852u	  s    rd  c                  C   sŒ   t  ttdt   tdt  dt   ddt    } t| tddd}|ttt  tttt    t dt  t  ddt   gksˆJ ‚d S )Nry   Fr¦  )r`   r]   r_   ra   r^   rB   rï  rp   rp   rq   Útest_issue_21942z	  s    6re  c                  C   sP   t td td  t d dd} t td td  t d dd}| |ksLJ ‚d S )Nru   rt   ry   F)ZcubicsTr¶   )r*   Zradrp   rp   rq   Útest_solver_flags€	  s      rf  N)rl   (  Zsympy.assumptions.askr   r   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.functionr   r   r   Zsympy.core.mulr	   Z
sympy.corer
   r   Zsympy.core.numbersr   r   r   r   r   r   Zsympy.core.relationalr   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   r   r   Zsympy.core.sympifyr   Z(sympy.functions.combinatorial.factorialsr   Z$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   rA  rU   Zsympy.polys.rootoftoolsrW   Zsympy.testing.pytestrX   rY   rZ   r[   Zsympy.core.randomr\   rÅ   r_  r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rr   r~   rƒ   r…   r†   r‡   r‰   r¨   rµ   r·   r¹   rº   r»   rË   rÌ   rÎ   rÔ   rÕ   rÖ   r×   rÙ   rÛ   rÜ   rÝ   rß   rá   râ   rñ   rO  rP  rd  rg  rh  rm  rs  rt  rv  rx  r|  r~  r  r€  r  r‰  r‹  rŒ  r  r¯  r°  r±  r³  r´  rµ  r¸  rÌ  rÍ  rÎ  rÑ  rÔ  rÝ  rÞ  rß  rà  rã  rå  rè  ré  rê  rì  rí  rî  rð  rñ  rò  rö  rü  rþ  rÿ  r  r  r  r	  r
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