U
    ˜9%e·¼  ã                   @   sÊ  d dl 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 d dlmZmZ d dlmZmZ 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mZ d dl m!Z! d dl"m#Z# d dl$m%Z% d dl&m'Z' d dl(m)Z)m*Z*m+Z+ d dl,m-Z- d dl.m/Z/m0Z0m1Z1m2Z2m3Z3 d dl4m5Z5 d dl6m7Z7 d dl8m9Z9 d dl:m;Z;m<Z<m=Z= d dl>m?Z? edƒ\Z@ZAZBZCZDZEZFZGZHZIZJeddd\ZKZLZMZNedƒZOedƒZPedƒZQdd„ ZRd d!„ ZSd"d#„ ZTe=d$d%„ ƒZUd&d'„ ZVd(d)„ ZWd*d+„ ZXd,d-„ ZYd.d/„ ZZd0d1„ Z[e;d2d3„ ƒZ\d4d5„ Z]d6d7„ Z^d8d9„ Z_d:d;„ Z`d<d=„ Zad>d?„ Zbd@dA„ ZcdBdC„ ZddDdE„ ZedFdG„ ZfdHdI„ ZgdJdK„ ZhdLdM„ Zie=dNdO„ ƒZjdPdQ„ ZkdRdS„ ZldTdU„ ZmdVdW„ ZndXdY„ ZodZd[„ Zpd\d]„ Zqd^d_„ Zrd`da„ Zsdbdc„ ZtddS )eé    )Ú
DerivativeÚFunctionÚSubsÚdiff)ÚEÚIÚRationalÚpi)ÚEq)ÚS)ÚSymbolÚsymbols)ÚimÚre)ÚexpÚlog)Úacosh)Úsqrt)Úatan2ÚcosÚsinÚtan)ÚIntegral)ÚPoly)ÚO)Úcollect)Úclassify_odeÚhomogeneous_orderÚdsolve)Úcheckodesol)Úclassify_sysodeÚconstant_renumberÚconstantsimpÚget_numbered_constantsÚ	solve_ics)Ú _undetermined_coefficients_match)ÚLinearCoefficients)Ú	ode_order)ÚXFAILÚraisesÚslow)Ú
filldedentzC0:11zu,x:zT©ÚrealÚfÚgÚhc                	   C   s    t tƒ td ƒ W 5 Q R X d S ©N)r)   Ú
ValueErrorr#   © r3   r3   ú_/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/solvers/ode/tests/test_ode.pyÚtest_get_numbered_constants0   s    
r5   c                  C   sØ  t tƒ t¡} t| dd}|d }|jjd d }|d }|jjd jd d }tt tƒtt	dtƒ ƒtt tƒtƒtt tƒtƒtt tƒtƒtt tƒtƒtt tƒtƒtt tƒtƒtt tƒtƒtt tƒtƒtt tƒtƒtt tƒtt	dtƒ ƒtt tƒtƒtt
t	dtƒt	d|ƒ |t tƒƒtƒtt tƒtƒtt tƒtƒtttƒtt	d| |t tƒt fƒ ƒtt tƒtƒtt	d|t tƒfƒtt	dtƒ ƒtt tƒtƒtt tƒtƒdddd	œ}||ks´t‚t| d
dtt tƒtƒksÔt‚d S )NÚall©ÚhintÚseparable_Integralé   r   Ú11st_homogeneous_coeff_subs_dep_div_indep_IntegraléÿÿÿÿÚnth_algebraic)ÚBernoulli_IntegralÚ1st_homogeneous_coeff_bestÚ	Bernoullir=   Únth_linear_euler_eq_homogeneousÚ%nth_linear_constant_coeff_homogeneousÚ	separableÚ(1st_homogeneous_coeff_subs_indep_div_depÚnth_algebraic_IntegralÚ
1st_linearÚ1st_linear_IntegralÚ	1st_exactÚ1st_exact_IntegralÚ	lie_groupÚ(1st_homogeneous_coeff_subs_dep_div_indepr;   Ú1st_power_seriesr9   Ú11st_homogeneous_coeff_subs_indep_div_dep_IntegralÚbestÚ	best_hintÚdefaultÚorderrN   )r.   Úxr   r   ÚlhsÚargsÚrhsr
   ÚC1r   r   r   ÚAssertionError)ÚeqÚoutputZsol1Z_yZ_u1Úexpectedr3   r3   r4   Útest_dsolve_all_hint5   s@    $& êr[   c                	   C   sB   t tƒ0 tttƒ t¡tttƒƒ tdƒdid W 5 Q R X d S )Nr:   ©Úics)r)   ÚNotImplementedErrorr   r.   rR   r   r   r3   r3   r3   r4   Útest_dsolve_ics[   s    
r_   c                     sÌ  t tt ƒ t ¡ tt ƒ ‰ tˆ dd} tˆ ddd}tˆ 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dddddddg}t|  ¡ ƒ|ks¢t‚| d tˆ tt ƒƒks¼t‚| d ttt ƒt	t  ƒksÚt‚tˆ ddttt ƒt	t  ƒksüt‚| d dkst‚| d dks t‚| d  
t¡r4t‚| d  
t¡rHt‚| d  
t¡r\t‚| d	  
t¡rpt‚| d  
t¡r„t‚| d  
t¡r˜t‚| d  
t¡s¬t‚| d  
t¡sÀt‚| d
  
t¡sÔt‚| d  
t¡sèt‚| d  
t¡süt‚t| ¡ ƒ|kst‚|d tˆ tt ƒƒks.t‚|d ttt ƒt	t  ƒksNt‚tˆ dddttt ƒt	t  ƒkstt‚|d dks†t‚|d dks˜t‚| d |d ks®t‚| d	 |d	 ksÄt‚| d |d ksÚt‚|d  
t¡rît‚|d  
t¡rt‚|d  
t¡rt‚|d	  
t¡r*t‚|d  
t¡r>t‚|d  
t¡rRt‚|d  
t¡sft‚|d  
t¡szt‚|d
  
t¡sŽt‚|d  
t¡s¢t‚|d  
t¡s¶t‚t| ¡ ƒ|ksÌt‚tt‡ fdd„ƒ tt‡ fdd„ƒ ttt ƒ t ¡dtt ƒd    ddd ttt ƒ t ¡dtt ƒd    ddksFt‚ttt ƒtt ƒ t ¡ tt ƒ t ¡ d tt ƒddttt ƒt	ttt ƒ t ¡ d ttdt ƒƒ t ƒ ttdt ƒ ƒ ƒksÈt‚d S )!Nr6   r7   F)r8   ÚsimplifyZall_IntegralrH   rI   r?   rK   r;   rD   rM   rF   rG   r@   r>   Úalmost_linearÚalmost_linear_IntegralrN   rO   rP   Ú
factorablerJ   rA   rQ   rC   r9   c                      s   t ˆ ddS )NZnotarealhintr7   ©r   r3   ©rX   r3   r4   Ú<lambda>Ÿ   ó    z%test_dsolve_options.<locals>.<lambda>c                      s   t ˆ ddS )NÚ	Liouviller7   rd   r3   re   r3   r4   rf       rg   r:   é   )rR   r.   r   r   ÚsortedÚkeysrW   r'   r
   rV   Úhasr   r)   r2   r   r   )ÚaÚbÚcrk   ZIntegral_keysr3   re   r4   Útest_dsolve_optionsa   sÂ              ÷
       û" &ÿ
ÿ
($ÿ
.ÿÿÿÿþrp   c                  C   s¤  t ttƒ td¡ttƒƒdks"t‚t ttƒttƒƒdks<t‚t tttƒ t¡dƒttƒƒdksbt‚t ttƒ t¡d ttƒƒdks†t‚t tttƒ t¡ttƒ tƒttƒƒ} t ttƒ t¡ttƒ ttƒttƒ  tttƒ  ttƒƒ}t ttƒ t¡ttƒ ttƒttƒ  tttƒ  ttƒƒ}| dks2t‚|dks@t‚|dksNt‚t dt ttƒ ttƒ t¡ d	t ttƒd   ttƒ ttƒƒd
ksœt‚dt dttƒ t¡ ttƒd  ttƒt  dtd   ttƒƒksæt‚ttdd„ ƒ t	dƒ}t ttƒ t¡|ttƒ |t ttƒ   dttƒ |ttƒ |t ttƒ    tttƒ t¡ |ttƒ |t ttƒ    t
 ttƒƒdks”t‚d}t tttƒt tƒtttƒtƒ ƒ|ksÆt‚t tttƒt tƒtttƒtƒ ttƒdd|ksþt‚t tdtd  ttƒ t¡ dƒttƒƒdks2t‚t tdttƒd  ttƒ t¡ dƒttƒƒdksjt‚t ttttƒtƒttƒt  dƒttƒƒdksžt‚tt tttƒdƒttƒddtƒsÆt‚tt tttƒ t¡dƒttƒdd ¡ ƒdddgks t‚t dt ttƒ ttƒ t¡ d	t ttƒd   ttƒ ttƒddd} t|  ¡ ƒddddd gksjt‚t ttƒ t¡tttƒt ƒ ttƒƒ} | d!ks t‚d S )"Nri   )r=   rB   rA   rh   Ú2nd_power_series_ordinaryrE   ÚLiouville_Integral)r=   rE   r   )r=   rC   rH   rF   r@   r?   rD   rK   rL   rJ   rB   rA   rE   r9   rI   rG   r>   rM   r;   )rc   r=   rC   rH   rF   r@   r?   rD   rK   rL   rJ   rA   rE   r9   rI   rG   r>   rM   r;   )rH   rF   r@   ra   rL   rJ   Ú3nth_linear_constant_coeff_undetermined_coefficientsÚ1nth_linear_constant_coeff_variation_of_parametersrI   rG   r>   rb   Ú:nth_linear_constant_coeff_variation_of_parameters_Integral)
rc   rF   r@   rL   rJ   rs   rt   rG   r>   ru   r:   )rc   rH   r@   ra   rJ   rI   r>   rb   ZRiccati_special_minus2é   éþÿÿÿc                   S   s&   t ttttƒ t¡ t¡ tttƒƒS r1   )r   rR   r.   Úyr   r3   r3   r3   r4   rf     s   ÿÿz#test_classify_ode.<locals>.<lambda>Úk)rc   rC   rH   rF   r@   rL   rJ   r9   rI   rG   r>   )rc   r=   rC   rH   rF   r@   r?   rD   rK   rL   rJ   rs   Z<nth_linear_euler_eq_nonhomogeneous_undetermined_coefficientsrt   Z:nth_linear_euler_eq_nonhomogeneous_variation_of_parametersrE   r9   rI   rG   r>   rM   r;   ru   ZCnth_linear_euler_eq_nonhomogeneous_variation_of_parameters_IntegralT)Úprep)rc   r=   rC   rH   rF   r@   rL   rJ   rA   rE   r9   rI   rG   r>   )rc   r=   rC   rH   rF   r@   rL   rJ   rE   r9   rI   rG   r>   )rL   rJ   é   ©ÚdictrP   rB   rQ   r@   ©r}   r8   r>   Úordered_hints)rC   rH   rL   rJ   r9   rI   )r   r.   rR   r   rW   r
   r   r)   r2   r   ÚzÚ
isinstancer}   rj   rk   )rm   rn   ro   ry   Úansr3   r3   r4   Útest_classify_ode©   st    ÿ
&$&<<
8 ÿþ
>ÿ
>ÿ,ÿÿÿþ
.&ÿÿ
(ÿ
,ÿ
(ÿ
((ÿ
J (rƒ   c                      sÎ  t tƒ tt¡t tƒ ‰ tdi‰tt‡ ‡fdd„ƒ tdƒdi‰tt‡ ‡fdd„ƒ t tƒdi‰tt‡ ‡fdd„ƒ t ddƒdi‰tt‡ ‡fdd„ƒ t dƒt tƒi‰tt‡ ‡fdd„ƒ t dƒt dƒi‰tˆ t tƒˆd	 t dƒdi‰tˆ t tƒˆd	 ttƒ t¡ td¡di‰tt‡ ‡fd
d„ƒ t tƒ t¡ tt¡di‰tt‡ ‡fdd„ƒ t tƒ t¡ td¡di‰tt‡ ‡fdd„ƒ t ttƒ t¡ td¡di‰tt‡ ‡fdd„ƒ t	t tƒttƒ td¡di‰tt‡ ‡fdd„ƒ t tƒ t¡ td¡t tƒi‰tt‡ ‡fdd„ƒ t tƒ t¡ td¡t tƒ t¡ td¡i‰tˆ t tƒˆd	 t tƒ t¡ td¡di‰tˆ t tƒˆd	 ttƒ t¡ tt¡di‰tt‡ ‡fdd„ƒ t tƒ t¡ tt¡di‰tt‡ ‡fdd„ƒ t ttƒ t¡ tt¡di‰tt‡ ‡fdd„ƒ t	t tƒtt
ƒ tt¡di‰tt‡ ‡fdd„ƒ t tƒ t¡ tt¡t tƒi‰tt‡ ‡fdd„ƒ t tƒ t¡ td¡t dƒi‰tˆ t tƒˆd	 t tƒ t¡ tt¡di‰tˆ t tƒˆd	 d S )Nr:   c                      s   t ˆ ttƒˆdS ©Nr\   ©r   r.   rR   r3   ©rX   r]   r3   r4   rf   N  rg   z'test_classify_ode_ics.<locals>.<lambda>r   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   X  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   \  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   `  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   d  rg   r\   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   u  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   y  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   }  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf     rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   …  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   ‰  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   ™  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf     rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   ¡  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   ¥  rg   c                      s   t ˆ ttƒˆdS r„   r…   r3   r†   r3   r4   rf   ©  rg   )r.   rR   r   r)   r2   r/   r   Úsubsrx   r   r€   r3   r3   r†   r4   Útest_classify_ode_icsH  sZ    	,rˆ   c            *      C   sN  t ddd\} }}}t ddd\	}}}}}}	}
}}t dtd\}}}}}}t dtd\}}}}}}}t dtd\}}}t d	ƒ}t||ƒ|ƒ}t||ƒ|ƒ}t|t| ||ƒ ƒ|||ƒ||ƒƒ ƒt||||ƒƒ|||ƒ||ƒƒ ƒf} d
d||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdid||ƒ||ƒgd|||ƒ||ƒƒ t| ||ƒ ƒ t||ƒ|ƒ |||ƒ||ƒƒ |||ƒƒ t||ƒ|ƒ g||ƒd||ƒdidœ}!t| ƒ|!ksôt‚t|||ƒd
 ||ƒ||ƒ  ƒt|||ƒ||ƒ ƒf}"d
d||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfd||ƒ d||ƒdfdd||ƒdfd||ƒ d||ƒdfdid||ƒ||ƒgd||ƒd
  t||ƒ|ƒ ||ƒ||ƒ  ||ƒ ||ƒ t||ƒ|ƒ g||ƒd||ƒdidœ}#t|"ƒ|#ks6t‚t||||ƒƒ|||ƒƒ |||ƒ||ƒ|ƒ ƒt||||ƒƒ|||ƒƒ |||ƒ||ƒ|ƒ ƒf}$||ƒ||ƒgdd|||ƒƒ |||ƒƒ |||ƒ||ƒ|ƒ t||ƒ|ƒ |||ƒƒ |||ƒƒ |||ƒ||ƒ|ƒ t||ƒ|ƒ gd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdi||ƒd||ƒdid
dœ}%t|$ƒ|%ksÀt‚t|||ƒ||ƒd  ƒt|||ƒd ƒf}&d
d||ƒdf||ƒd  d||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdid||ƒ||ƒgd||ƒ ||ƒd  t||ƒ|ƒ ||ƒd  t||ƒ|ƒ g||ƒd||ƒdidœ}'t|&ƒ|'ksät‚t|||ƒ||ƒ t|ƒd
  ƒt|||ƒd
 t|ƒd
  ƒf}(d
d||ƒdf||ƒ t|ƒd
  d||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdfdd||ƒdf||ƒ t|ƒd
  d||ƒdfdid||ƒ||ƒgd||ƒ ||ƒ t|ƒd
  t||ƒ|ƒ ||ƒd
  t|ƒd
  t||ƒ|ƒ g||ƒd||ƒdidœ})t|(ƒ|)ksJt‚d S )Nz
k, l, m, nT)ÚIntegerz"k1, k2, k3, l1, l2, l3, m1, m2, m3zP, Q, R, p, q, r©ÚclszP1, P2, P3, Q1, Q2, R1, R2zx, y, zÚtri   r   r:   Ztype2F)Úno_of_equationÚ
func_coeffÚtype_of_equationÚfuncÚ	is_linearrX   rQ   r<   Ztype3Ztype4)r   r‘   r   rX   rŽ   rQ   r   rv   r{   Ztype1)	r   r   r   r
   r   r   r    rW   r   )*ry   ÚlÚmÚnÚk1Úk2Zk3Úl1Úl2Úl3Úm1Úm2Zm3ÚPÚQÚRÚpÚqÚrZP1ZP2ZP3ZQ1ZQ2ZR1ZR2rR   rx   r€   rŒ   Úx1Úy1Úeq6Zsol6Úeq7Zsol7Zeq8Zsol8Zeq11Zsol11Zeq13Zsol13r3   r3   r4   Útest_classify_sysode³  sê     L:       ÿ  8ÿ
ÿÿý8: 
    
  ÿ  :ÿýdfÿ8       ÿ ý,6         ÿ   "ÿý@>         ÿ   ÿ&ÿýr¦   c                  C   sÌ	  t ttƒ t¡dttƒ  ttƒtdƒdidtttƒtdt d ƒƒksNt‚t ttƒ t¡ttƒ ttƒtdƒdidtttƒttƒƒkst‚t ttƒ t¡ttƒ ttƒttƒ t¡ td¡didtttƒttƒƒksàt‚t ttƒ tt¡ttƒ ttƒtdƒdttƒ t¡ td¡didtttƒt	tƒt
tƒ ƒksDt‚t ttƒ t¡ttƒ ttƒ ttƒ t¡ttƒ ttƒ gttƒttƒgtdƒdtdƒdidtttƒttƒt
tƒ ƒtttƒttƒt	tƒ ƒgksàt‚td ttƒd  t  t¡} t | ttƒtdƒdidtttƒttd ƒ t ƒtttƒttd ƒt ƒgksTt‚t | ttƒttƒ t¡ td¡didtttƒtttj ƒ t ƒtttƒtttj ƒt ƒgks¼t‚t
ttƒƒtt	ttƒƒ ttƒd  ttƒ t¡  } t | ttƒtdƒdidddttt
ttƒƒ ttƒd d  tddƒƒksBt‚t | ttƒtdƒdidd	dttt
ttƒƒ ttƒd d  tddƒƒks’t‚ttttƒtttƒ ƒgttƒgtgtdƒdiƒtdiksÒt‚ttttƒtt	tƒ tt
tƒ  ƒgttƒgttgtdƒdttd ƒdiƒtdtdiks0t‚ttttƒtt	tƒ tt
tƒ  ƒgttƒgttgtdƒdttƒ t¡ td¡diƒtdtdiks˜t‚ttttƒtt	tƒ tt
tƒ  ƒgttƒgttgtdƒdiƒtdiksæt‚tt ttƒ t¡ttƒ td¡t  tdƒdttƒ t¡ td¡didƒtttƒdƒtttƒtd d
 td  ƒhksdt‚tt ttƒ t¡ttƒ td¡t  tdƒdidƒtttƒdƒtttƒtt td d
  ƒhksÌt‚tdƒ\}}}tttƒ|| t|t ƒ | | |t|t ƒ | |  d   ƒ}t tttƒ t¡|ttƒ dttƒ|   ƒttƒtdƒ|id|kslt‚tt ttƒ t¡ttƒ td¡t  ttƒ t¡ td¡dtdƒdidƒtttƒdƒtttƒtd d
 ƒhksât‚tt ttƒ t¡ttƒ td¡t  tdƒdttƒ t¡ td¡didƒtttƒdƒtttƒtd d
 ƒhksXt‚ttdd„ ƒ ttdd„ ƒ tdƒ\}}}tttƒttt  ttd   ttd   |td  d|   ƒg}ttƒg}	ttttg}
tdƒdttƒ t¡ td¡dt|ƒ |d¡dt|ƒ |d¡di}tdƒdttƒ t¡ td¡dtttƒ td¡t|ƒdtttƒ td¡t|ƒdi}t||	|
|ƒ}t||	|
|ƒ}||  krÒtdtdt|d | d|  t| | d
|  iksØn t‚tdƒtdƒi}t ttƒ t¡ttƒ ttƒ|dtttƒtdƒttƒ ƒk	s,t‚ttƒ t¡ td¡ttƒ t¡ td¡tdƒtdƒi}t ttƒ tt¡ttƒ ttƒ|dtttƒtdƒt
tƒ ttƒ t¡ td¡t	tƒ  ƒk	sÈt‚d S )Nr:   ri   r\   r   rH   F)r]   r8   r`   rv   Té   zK r f0c                   S   sH   t tttƒtttƒ tttƒ  ƒgttƒgttgtdƒdttƒdiƒS )Nr   r:   )	r$   r
   r.   rR   rV   r   ÚC2r   r	   r3   r3   r3   r4   rf     rg   z test_solve_ics.<locals>.<lambda>c                   S   sD   t tttƒtttd  ƒƒgttƒgtgttƒ t¡ td¡diƒS )Nri   r   )r$   r
   r.   rR   r   rV   r   r‡   r3   r3   r3   r4   rf     rg   zEI q Lé   é   )r   r.   rR   r   r
   r   rW   r   r‡   r   r   r/   r   ÚHalfr   r$   rV   r¨   r	   Úsetr   r)   r2   ÚC3ÚC4r   )rX   ÚKr¡   Zf0ÚsolZEIr    ÚLZsolsÚfuncsÚ	constantsZics1Zics2Zsolved_constants1Zsolved_constants2r]   r3   r3   r4   Útest_solve_icsâ  sà    .ÿBP& ÿÿ
< ÿ2ÿ
 ÿÿ.ÿÿ6

  ÿ*ÿ


  ÿ*ÿ
@2ÿ
ÿ
2 ÿ
ÿ
>ÿ
J*ÿ
4*ÿ
FLJ"ÿ
J"ÿ
D
   ý   ý    üD8$6ÿr´   c                  C   s^  t dƒ} t dƒ}tdƒ}td| t| |ƒƒ | |ƒƒdks>t‚t|t| |ƒ|ƒ d| | |ƒ  t|ƒ|  | |ƒƒdks~t‚t|d | |ƒ ||¡ |t| |ƒ|ƒ  | |ƒ | |ƒƒdksÂt‚tt|t| |ƒƒ ||ƒ| |ƒƒdksìt‚tt|t|t| |ƒƒ ||ƒ |ƒ| |ƒƒdks"t‚tt| |ƒ||ƒ||ƒƒdksFt‚tt| |ƒ||ƒt||ƒ|ƒ | |ƒƒdksxt‚tt| |ƒ||ƒt||ƒ|ƒ ||ƒƒdksªt‚tt|t|t| |ƒƒ ||ƒ |ƒ||ƒƒdksàt‚tt|| |ƒ |ƒ| |ƒƒdkst‚t|tt|| |ƒd  ||ƒƒ | |ƒƒdks:t‚tt|t|t| |ƒƒ ||ƒ |ƒ||ƒƒdkspt‚tt| |ƒ||ƒ||ƒƒdks”t‚tt|t| |ƒƒ ||ƒ| |ƒƒdksÀt‚tt| |ƒ||ƒt||ƒ|ƒ ||ƒƒdksòt‚tt|t| |ƒ||ƒ |ƒ| |ƒƒdks t‚t|tt|t| |ƒ|ƒd  ||ƒƒ | |ƒƒdksZt‚d S )Nr.   r/   rR   rv   r   r:   ri   )r   r   r'   r   rW   r   r   r   )r.   r/   rR   r3   r3   r4   Útest_ode_order=  s2    &@D*6$226&46$,2.$ ÿÿrµ   c                  C   sh  t ttt ƒttt ƒ ttƒdks(t‚t td ttƒttƒ  ttƒd ksPt‚t tt tttt ƒ  ttƒdksxt‚t tt ttd td  ƒ td t	tƒt	tƒ   t
ttddƒ  ttƒd   ttƒtddƒksàt‚t tt ttt ƒ tt ttt ƒ  ttt ƒ ttƒdks&t‚t ttƒtttƒƒdksDt‚t ttƒd tttƒƒdksft‚t tt t ttƒdks„t‚t tt t tttƒdks¤t‚t td ttƒ ttd ttƒd  ƒ ttƒƒd ksàt‚t tttƒd ttttƒtƒdkst‚t tttƒd tttƒtƒd ks.t‚t tttƒd ttttƒƒd ksTt‚t tttƒd tttttƒƒd ks|t‚t ttƒttƒtƒd ksšt‚t ttƒ t dtttƒt ƒ  ttƒtƒdksÒt‚t t	dt ƒt	td ƒ ttƒd ksüt‚t t	dt ƒt	tƒ ttƒdks"t‚t t	tt ƒttƒdks@t‚t dt	dt ƒ dt	tƒ  ttƒdksnt‚tdƒ} t | t	dt ƒ | t	tƒ  ttƒdks¤t‚t ttƒ t¡ttƒd ksÄt‚t ttƒ t¡ t ttƒd ksêt‚t ttƒttƒd kst‚t tttd ƒ ttƒd ks&t‚t tt
 tƒt
ks>t‚t tt tƒd ksVt‚ttd	d
„ ƒ d S )Nr   ri   r:   r©   rv   r<   r§   rm   c                   S   s   t tt ƒS r1   )r   rR   rx   r3   r3   r3   r4   rf   u  rg   z(test_homogeneous_order.<locals>.<lambda>)r   r   rx   rR   r   rW   r   r   r   r   r	   r   r.   r€   r   r   r   r)   r2   )rm   r3   r3   r4   Útest_homogeneous_orderW  sH    (((4ÿ ÿÿF" <(&&(8*&.. &"r¶   c                  C   s:   t dt ƒ} t| ƒt| ƒ }}| t¡r6| t¡r6t‚d S )Nr:   )r   rR   r   r   rl   r   rW   )rx   Úir¡   r3   r3   r4   Ú)test_noncircularized_real_imaginary_partsx  s    r¸   c                  C   s.   dt td ƒ } | t| t td ƒƒks*t‚d S )Nr:   ri   rv   )r   rR   r   rW   )r°   r3   r3   r4   Ú$test_collect_respecting_exponentials‚  s    r¹   c                  C   s|  t ttƒtƒddikst‚t tdt tdƒ ƒtƒdtdt tdƒ ƒtdt tdƒ ƒhdœksft‚t ttƒttƒ tƒddiksˆt‚ttƒtttƒ td ttƒ td ttƒ tttƒ ttƒh} t ttƒtd t d  tƒd| dœksôt‚t ttƒtd  ttƒt  ttƒ tƒd| dœks.t‚t tdt ƒttƒ td t d  tƒdtdt ƒttƒ td tdt ƒ ttƒ ttƒtdt ƒ td ttƒ tdt ƒ tttƒ tdt ƒ ttdt ƒ ttƒ hdœksìt‚t dttƒ tƒddikst‚t ttƒtƒddiks(t‚t dt td t d  tƒddt tdt  td dt  hdœkstt‚t tt	 tƒddikst‚t ttƒtdt d ƒ tƒdtddt  ƒhdœksÌt‚t ttƒtd t d  tƒdtttƒ tttƒ td ttƒ td ttƒ ttƒttƒhdœks6t‚t ttƒtttƒ  tƒddiks^t‚t ttƒttdt ƒ  tƒddiksŠt‚t ttƒt
tƒ tƒddiks®t‚t td ttƒ ttƒ tttƒ  t tƒdtd ttƒ ttƒ tttƒtjttƒttƒ ttƒtttƒ ttƒ tttƒ tttƒ ttƒ tttƒ ttƒttƒ td ttƒ ttƒ hdœks~t‚t d	t ttd ƒ tƒtttd ƒ tttd ƒ ttd ƒttd ƒhdd
œksØt‚t dt t tƒddt tdt  hdœks
t‚t dt tdt ƒ tƒddt tdt ƒ hdœksFt‚t tt ƒt tƒddiksht‚t td	ƒtƒdtjhdœksŠt‚t dttƒ tƒdttƒhdœks²t‚t ttt ƒtƒdttt ƒhdœksÞt‚t ttƒtƒdttƒttƒhdœkst‚t ttƒtƒdttƒttƒhdœks2t‚t ddttƒ  dttƒ  tƒdtjttƒttƒttƒhdœkszt‚t td tƒdtjttd hdœks¤t‚t dt ttƒ tt ƒ tƒdtttƒ ttƒtt ƒhdœksìt‚t dtdt ƒ ttƒ tƒdtdt ƒttƒ ttƒtdt ƒ hdœks>t‚t tttƒ tƒdtjtttƒttƒhdœksrt‚t td dt  tƒdtjttd hdœks¤t‚t d	t ttƒ tƒdtttƒ tttƒ ttƒttƒhdœksêt‚t ttdt ƒ tƒdttdt ƒ ttdt ƒ tdt ƒtdt ƒhdœks@t‚t td tt ƒ tƒdttt ƒ td tt ƒ tt ƒhdœksŒt‚t dtt ƒ td tt ƒ  tƒdttt ƒ td tt ƒ tt ƒhdœksæt‚t tdt ƒtd  tƒdtjttd tdt ƒhdœk	s&t‚t ttt ƒ tƒdttt ƒ tt ƒhdœk	s^t‚t ttdt ƒ tƒdtjttdt ƒhdœk	s”t‚t ttƒtt ƒ tƒdttƒttƒtt ƒhdœk	sÐt‚t ttƒtƒdttƒhdœk	sôt‚t tjtdt ƒd  tƒdtjtdt ƒtdt ƒhdœk
s8t‚t tdt ƒtjtdt ƒd   tƒdtdt ƒtdt ƒ tdt ƒtdt ƒ tdt ƒhdœk
s¦t‚t dt ttƒ ttƒ tƒdtjtttƒttƒhdœk
sæt‚t ttƒd tdt ƒd  tƒdttƒtdt ƒttƒtdt ƒhdœks8t‚t ttd ƒtƒddiksXt‚t dtd  tƒddiksxt‚d S )NÚtestFri   r{   T)rº   Útrialsetr:   rv   r©   )r»   rº   é   é   r§   é	   rw   )r%   r/   rR   rW   r   r   r   r   r   rx   r   r   ZOner   r«   )Úsr3   r3   r4   Ú$test_undetermined_coefficients_match‰  sT   &ÿÿÿ@ÿ" ÿÿ
" ÿ ,  þÿþ
 &ÿ
ÿ
$  ÿÿ
ÿ
ÿ
ÿ
& ÿ "   
 
  þÿþ
2þÿ
ÿ
ÿ
ÿ
ÿ
ÿ
ÿ
ÿ
 ÿ
ÿ
 ÿ
,ÿ
ÿ
ÿ
(ÿ
2ÿÿ
,ÿ
$,ÿ
ÿ
ÿ
ÿ
ÿ
ÿ
 ÿ
  ÿ ,
ÿÿþ
ÿ
 (ÿ
 rÀ   c                  C   sª   ddl m}  t| ttttƒtƒ ttƒ   tttƒtƒ ttƒ d }t|ttƒƒdks^t‚td ttƒd  ttƒ t¡ dt ttƒ  }t|ttƒƒdks¦t‚d S )Nr   )ÚAri   )rc   rH   rF   r@   ra   rL   rJ   rs   rt   rI   rG   r>   rb   ru   )
rc   rH   r?   rD   rK   rL   rJ   rI   rM   r;   )Z	sympy.abcrÁ   rR   r   r.   r   rW   )rÁ   rX   r3   r3   r4   Útest_issue_4785_22462ø  s
    <2rÂ   c                   C   sˆ   t tdd„ ƒ ttttƒ t¡ttttƒ  ttƒdddd ddœksJt‚t tdd„ ƒ tttƒ t¡ttƒdddd ddœks„t‚d S )	Nc                   S   s(   t tttƒ t¡ttttƒ  ttƒƒS r1   )r   r.   rR   rx   r   r3   r3   r3   r4   rf     rg   z!test_issue_4825.<locals>.<lambda>Tr|   r   r3   )rQ   rP   r   c                   S   s   t ttƒ t¡ttƒƒS r1   )r   r.   rR   r   rx   r3   r3   r3   r4   rf     rg   )r)   r2   r   r.   rR   rx   r   rW   r3   r3   r3   r4   Útest_issue_4825  s    *
ÿ
ÿrÃ   c                  C   s¦   ddl m}  ttt tt  ƒttt tt  ƒ  krLtt tt  ksRn t‚ttt  tt  }| tttgdƒD ]*\}}}t||t  |t  ƒ|ksvt‚qvd S )Nr   )Ú
variationsrv   )	Zsympy.utilities.iterablesrÄ   r!   rV   rR   r¨   rx   rW   r­   )rÄ   Úerm   rn   ro   r3   r3   r4   Ú'test_constant_renumber_order_issue_5308  s    ÿþrÆ   c                  C   sâ   t dƒ\} }}}|| | | ||  g}t|d ƒ|| ks@t‚t|d |gdt| ks^t‚t|d |gtgdt| ks€t‚t|||gdt| t| t|  gks¬t‚t|||gt dƒdt| t| t|  gksÞt‚d S )Nze1:3 x yr   )Ú	variables)rÇ   ZnewconstantszC3:5)r   r!   rW   rV   r¨   r­   r®   )Úe1Úe2rR   rx   Úexprsr3   r3   r4   Útest_constant_renumber#  s    ",rË   c                  C   sl  t ddd} t dƒ}tdƒ}t||ƒ |d¡| d ||ƒ  ||ƒƒ}tdd„ |jD ƒƒdksbt‚ttt	t
ƒ tt	t
ƒ  tt
ƒ tthƒtt	t
ƒ tt
ƒ ks¤t‚ttt	t
ƒ tt	t
ƒ  ttt
ƒ  ttthƒtt	t
ƒ ttt
ƒ  ksðt‚tttt
 ƒthƒttt
ƒ kst‚tt
t t tthƒtt
 ks:t‚tt
t tt
t
d	d
fƒ thƒtt
 ksht‚d S )Nry   Tr,   rŒ   Úwr§   c                 S   s   g | ]}|j  d ¡r|‘qS )ÚC)ÚnameÚ
startswith)Ú.0r¿   r3   r3   r4   Ú
<listcomp>3  s      z#test_issue_5770.<locals>.<listcomp>r:   ri   )r   r   r   r   ÚlenZfree_symbolsrW   r"   rV   r   rR   r¨   r   r­   r   rx   r   )ry   rŒ   rÌ   r°   r3   r3   r4   Útest_issue_5770.  s    *(ÿ.ÿ&$rÓ   c                   C   s@   t ttƒ ttƒ tƒd ks t‚t tttƒ ttƒd ks<t‚d S r1   )r   r   rR   r   rW   rx   r3   r3   r3   r4   Útest_issue_5112_5430=  s     rÔ   c                      s   t dƒ‰ tt‡ fdd„ƒ d S )Nr.   c                      s   t ˆ tƒ t¡d ˆ tƒdƒS )Nri   Zfdsjf)r   rR   r   r3   ©r.   r3   r4   rf   D  rg   z!test_issue_5095.<locals>.<lambda>)r   r)   r2   r3   r3   rÕ   r4   Útest_issue_5095B  s    rÖ   c                  C   s¼  t dƒ} tt| tƒ ƒ}tdt d| tƒ  ƒ}tt| tƒ tddƒ ƒ}tdt d| tƒ  d| tƒ dt   ƒ}tdtd  d| tƒd   ƒ}tdt d| tƒ  d| tƒ dt   tdtd  d| tƒd   ƒ ƒ}tdt d| tƒ td   ƒ}t|t| tƒƒd kst	‚t|t| tƒƒdks6t	‚t|t| tƒƒd ksPt	‚t|t| tƒƒdksjt	‚t|t| tƒƒdks„t	‚t|t| tƒƒdksžt	‚t|t| tƒƒd ks¸t	‚d S )Nr.   rv   r©   r{   é   ri   r   )
r   r   rR   r   r   r   r   r   r   rW   )r.   Úeq1Úeq2Úeq3Úeq4Úeq5r¤   r¥   r3   r3   r4   Útest_homogeneous_functionG  s    , L rÝ   c                  C   sä  t dt dttƒ  d  t dt dttƒ  d   } }| | }t|ƒt| ¡ ƒ }t|ƒ}|}t|ƒ}tt|ƒƒ}t|ƒ}dtddƒf}	| 	|ttƒ¡|	ks¤t
‚| 	|ttƒ¡|	ks¼t
‚| 	|ttƒ¡|	ksÔt
‚dt ttƒ }
t|
ƒ}dt d t }t|ƒ}dt dttƒ  d	 dt dttƒ  d  }t|ƒ}dt dttƒ  tdƒ dt dttƒ  d  }t|ƒ}| 	|
ttƒ¡d ks’t
‚| 	|ttƒ¡d ks¬t
‚| 	|ttƒ¡d ksÆt
‚| 	|ttƒ¡d ksàt
‚d S )
Nri   rv   r{   r×   r¾   é   r©   ióÿÿÿr:   )r€   rR   r.   r   r   Úexpandr&   r   r   Z_linear_coeff_matchrW   r   )r”   ÚdÚratrØ   Zobj1rÙ   Úobj2rÚ   Zobj3r‚   rÛ   Zobj4rÜ   Zobj5r¤   Zobj6r¥   Zobj7r3   r3   r4   Útest_linear_coeff_matchY  s0    :04rã   c                  C   s>   t tƒd } tttt tƒ|  | t  tgƒƒjƒdks:t‚d S )Nri   )r   rV   rÒ   r   r"   rR   ZgensrW   )ro   r3   r3   r4   Útest_constantsimp_take_problemy  s    rä   c                  C   sº  t dƒ} ttƒ t¡ttƒ }tttƒ| | t  | td  d  | td  d  | td  d  | td  d  ttd ƒ ƒ}t|d	d
|ks”t‚t||ddd sªt‚ttƒ t¡tttƒ  }tttƒ| td  d | td  d  |  ttd ƒ ƒ}t|d	d
|kst‚t||ddd s,t‚ttƒ t¡t	tttƒ ƒ }tttƒtd d dt	dƒ  t
dƒ td t	dƒ  d ttd ƒ ƒ}t|d	tdƒdidd|ks¶t‚d S )NrV   ri   rv   r§   r©   rª   r{   éx   rL   r7   r:   )rQ   r   r½   )r8   r]   r”   )r   r.   rR   r   r
   r   r   rW   r   r   r   )rV   rX   r°   r3   r3   r4   Útest_series~  s     Bÿ
ÿ:Jræ   c                  C   s4  t dƒ\} }ttƒ td¡tttƒ  }t|ƒdks8t‚tttƒ|td d d  | t td d d   ttd ƒ ƒ}t|dd	|ksŽt‚t	||ƒd
ks t‚tttƒ|td d d td d d  td d  d  | ttd d d  td d d  t
dƒ   ttd ƒ ƒ}t|ddd|ks2t‚tttƒ|t |  ttd ƒ ƒ}t|ddd|kslt‚t	||ƒd
ks€t‚dtd  ttƒ td¡ dt ttƒ t¡  dttƒ  }t|ƒdksÐt‚tttƒ|td  d td  d  | t  ttd ƒ ƒ}t|dd	|ks"t‚t	||ƒd
ks6t‚ttƒ td¡tttƒ t¡  ttƒ }t|ƒdksrt‚tttƒ|td d td d  d  | t td  d d   ttd ƒ ƒ}t|ƒ|ksÔt‚ttƒ td¡ttƒ t¡ tttƒ  }t|ƒdkst‚tttƒ|td  d td d  d  | t td d td d  td  d   ttd ƒ ƒ}t|ƒ|ks†t‚ttƒ td¡tttƒ  }t|ƒdks´t‚tttƒ|td d td d  d  | t td  d d   ttd ƒ ƒ}t|ddd|kst‚t	||ƒd
ks0t‚d S )NzC1 C2ri   )Z2nd_linear_airyrq   rv   r§   r:   r¼   rq   r7   ©Tr   r©   rw   )r8   Zx0)r8   r”   )rc   Z2nd_hypergeometricZ2nd_hypergeometric_Integralrq   )rc   rq   r½   )rq   rª   é´   r×   )r   r.   rR   r   r   rW   r
   r   r   r   r   )rV   r¨   rX   r°   r3   r3   r4   Útest_2nd_power_series_ordinary’  sJ    B:.ÿ
þ"><*P*(*ÿ
ÿPré   c                  C   s  t dƒ\} }}td ttƒ td¡ dt ttƒ t¡  dt d ttƒ  }tttƒ| td  dtd  d dtd   dt  d  ttd ƒ ƒ}t|d	d
|ks®t‚t||ƒdksÀt‚dtd  ttƒ td¡ dtd  ttƒ t¡  dtd  d ttƒ  }tttƒ| t	tƒ td d td d  td d  t d  ttd ƒ ƒ}t|d	d
|ksrt‚t||ƒdks†t‚td ttƒ td¡ td ttƒ t¡  td d ttƒ  }tttƒ| td  d dtd  d  td d  td d  td  d  t |td  td  d td d  td  d   ttd ƒ ƒ}t|ƒ|kslt‚t||ƒdks€t‚td ttƒ td¡ tttƒ t¡  td t
ddƒ ttƒ  }tttƒ| td d td d  d  t	tƒ |t	tƒ td d td d  d   ttd ƒ ƒ}t|d	d
|ks@t‚t||ƒdksTt‚tttƒ td¡ ttƒ t¡ |t ttƒ  }tttƒ| |d td  d |td  d  d  ttd ƒ ƒ}t|ttƒd	d
|ksät‚t||ƒdksøt‚ttƒ td¡dt t ttƒ t¡  |t ttƒ  }tttƒ| | td  |d  |d  |d  |d  d |td  |d  |d  |d  d  |td  |d  |d  d  |td  |d  d  |t  d  ttd ƒ ƒ}t|ttƒd	d
|kst‚t||ƒdkst‚d S )NzC1 C2 ari   rv   r©   iðÿÿÿr¾   r:   r§   Z2nd_power_series_regularr7   rç   r½   rª   iÐ  r{   éP   é<   é   rå   é@   i@8  i@  é$   )r   rR   r.   r   r
   r   r   rW   r   r   r   )rV   r¨   rm   rX   r°   r3   r3   r4   Útest_2nd_power_series_regularÅ  sh    BJ>ÿÿN,
 ÿP0ÿ
ÿD.&ÿ
ÿ2B::&ÿÿþþþ
þrï   c                  C   s4   t dƒ} t dƒ}tt dƒtdƒ| ƒ ƒ|ks0t‚d S )NrŒ   r­   rV   r¨   )r   r#   r   rW   )rŒ   r­   r3   r3   r4   Útest_issue_15056ì  s    rð   c                  C   sÚ   t  t dt ttƒ  ttƒ tttƒtƒ } tttd t ƒ ttd t ƒtt ttd  t ƒ t tƒ  }t| |ƒdks†t‚t ttt t	 ƒ  }tt	ttƒ tƒttƒ 
td¡ } t| |ttƒƒdksÖt‚d S )Nri   rç   )rV   rR   r.   r   r¨   r   r   r   rW   rx   r   ©rX   r°   r3   r3   r4   Útest_issue_15913ò  s    0D"rò   c                   C   s    t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s4   t ttƒ t¡ttƒ t¡gttƒttƒttƒgƒS r1   )r   r.   rR   r   r/   r0   r3   r3   r3   r4   rf   ü  rg   z"test_issue_16146.<locals>.<lambda>c                   S   s(   t ttƒ t¡ttƒ t¡gttƒgƒS r1   )r   r.   rR   r   r/   r3   r3   r3   r4   rf   ý  rg   )r)   r2   r3   r3   r3   r4   Útest_issue_16146û  s    ró   c                  C   sö   t tƒd t tƒ t¡ } tt tƒtƒ}t| ƒ|ks8t‚t tƒttƒ t tƒ td¡ } tt tƒttt  ƒtt tƒttƒƒh}t	t| ƒƒ|ks”t‚t tƒd dt tƒ  d t tƒ td¡ } tt tƒttt  t
td   ƒ}t| ƒ|ksòt‚d S )Nri   r:   rv   )r.   rR   r   r
   rV   r   rW   r   r¨   r¬   r­   rñ   r3   r3   r4   Ú&test_dsolve_remove_redundant_solutions   s     (,"rô   c                  C   s~   t dtd\} }tdƒ}tt| |ƒ|ƒ| |ƒ||ƒ ƒtt||ƒ|ƒ| |ƒ||ƒ ƒg}t|ƒ}t||ƒdddgfkszt‚d S )NzA BrŠ   rŒ   Tr   )r   r   r   r
   r   r   r   rW   )rÁ   ÚBrŒ   rX   r°   r3   r3   r4   Útest_issue_13060  s
    @rö   c                  C   sÄ   t dƒ\} }tdƒ}d|  t| d ƒ ||ƒ d|d  | d  | d| | d   d  t||ƒ|dfƒ  }t|ddd	}|d
 d dkst‚t dƒ\}}t|d
d}t|ƒttdƒƒksÀt‚d S )NzN sÚrhog      @r:   r©   ri   Tr6   r~   rq   Ztermsr{   zC1,C2r7   aö  
        Eq(rho(s), C2*(1 - 4.0*s**4*sqrt(N - 1.0)/N + 0.666666666666667*s**4/N
        - 2.66666666666667*s**3*sqrt(N - 1.0)/N - 2.0*s**2*sqrt(N - 1.0)/N +
        9.33333333333333*s**4*sqrt(N - 1.0)/N**2 - 0.666666666666667*s**4/N**2
        + 2.66666666666667*s**3*sqrt(N - 1.0)/N**2 -
        5.33333333333333*s**4*sqrt(N - 1.0)/N**3) + C1*s*(1.0 -
        1.33333333333333*s**3*sqrt(N - 1.0)/N - 0.666666666666667*s**2*sqrt(N
        - 1.0)/N + 1.33333333333333*s**3*sqrt(N - 1.0)/N**2) + O(s**6)))	r   r   r   r   r   rW   r   r+   Ústr)ÚNr¿   r÷   ZeqnÚmatchrV   r¨   r°   r3   r3   r4   Útest_issue_22523  s    Dÿrû   c                  C   s$  t dtd\} }t ddd\}}}}}d\}}}}t|t| |ƒ|dƒ || |ƒ  |||ƒ| |ƒ   dƒ}t|t||ƒ|dƒ |||ƒ| |ƒ   dƒ}||g}	t|	| |ƒ||ƒg| dƒd| |ƒ ¡  |d¡d|dƒd	||ƒ ¡  |d¡did
\}
}|
t| |ƒtdtdƒ ƒtdƒdtdƒ   ttdƒ| tdtdƒ ƒ d ƒ d dtdƒ tdƒ ttdƒd ƒ ttdƒ| ttdƒd ƒ d ƒ d  ƒks¤t‚|t||ƒtdƒd ttdƒ| tdtdƒ ƒ d ƒ d dtdƒ ttdƒ| ttdƒd ƒ d ƒ d  ƒks t‚d S )Nzx1, x2rŠ   zt k1 k2 m1 m2Tr,   )r:   r:   r:   r:   ri   r   r:   r\   rv   r{   é
   rì   éûÿÿÿ)	r   r   r
   r   r   r‡   r   r   rW   )r¢   Zx2rŒ   r•   r–   rš   r›   rØ   rÙ   ZeqsZx1solZx2solr3   r3   r4   Útest_issue_22604-  s     :..   ÿTJÿrþ   c                  C   s€   t ttƒ t¡dttƒd  dttƒ d  ƒt ttƒ t¡dttƒd  dttƒ d  ƒfD ]} dt| ttƒƒks`t‚q`d S )	Niìÿÿÿri   iô  i   rw   r{   r×   r@   )r
   r.   rR   r   r   rW   )Úder3   r3   r4   Útest_issue_22462;  s    ..þr   c                  C   sP   t dƒ} tdƒ}tt|   || ƒ ¡  ¡  || ƒ ¡  dƒ}t|ƒdksLt‚d S )NrR   rx   r   )rh   Znth_order_reduciblerq   rr   )r   r   r
   r   r   r   rW   )rR   rx   rX   r3   r3   r4   Útest_issue_23425B  s    ,ÿr  N)uZsympy.core.functionr   r   r   r   Zsympy.core.numbersr   r   r   r	   Zsympy.core.relationalr
   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z$sympy.functions.elementary.complexesr   r   Z&sympy.functions.elementary.exponentialr   r   Z%sympy.functions.elementary.hyperbolicr   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   r   r   Zsympy.integrals.integralsr   Zsympy.polys.polytoolsr   Zsympy.series.orderr   Zsympy.simplify.radsimpr   Zsympy.solvers.oder   r   r   Zsympy.solvers.ode.subscheckr   Zsympy.solvers.ode.oder    r!   r"   r#   r$   Z sympy.solvers.ode.nonhomogeneousr%   Zsympy.solvers.ode.singler&   Zsympy.solvers.deutilsr'   Zsympy.testing.pytestr(   r)   r*   Zsympy.utilities.miscr+   ZC0rV   r¨   r­   r®   ZC5ZC6ZC7ZC8ZC9ZC10ÚurR   rx   r€   r.   r/   r0   r5   r[   r_   rp   rƒ   rˆ   r¦   r´   rµ   r¶   r¸   r¹   rÀ   rÂ   rÃ   rÆ   rË   rÓ   rÔ   rÖ   rÝ   rã   rä   ræ   ré   rï   rð   rò   ró   rô   rö   rû   rþ   r   r  r3   r3   r3   r4   Ú<module>   s‚   &
G  k/[!
	o
 
2'	