o
    *Î®c·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   s6   t tƒ td ƒ W d   ƒ d S 1 sw   Y  d S ©N)r)   Ú
ValueErrorr#   © r3   r3   úG/tmp/pip-target-vg8gfxp4/lib/python/sympy/solvers/ode/tests/test_ode.pyÚtest_get_numbered_constants0   s   

"ÿr5   c               
   C   s  t tƒ t¡} t| dd}|d }|jjd d }|d }|jjd jd d }i dtt tƒtt	dtƒ ƒ“dtt tƒtƒ“d	tt tƒtƒ“d
tt tƒtƒ“dtt tƒtƒ“dtt tƒtƒ“dtt tƒtƒ“dtt tƒtƒ“dtt tƒtƒ“dtt tƒtƒ“dtt tƒtt	dtƒ ƒ“dtt tƒtƒ“dtt
t	dtƒt	d|ƒ |t tƒƒtƒ“dtt tƒtƒ“dtt tƒtƒ“dtttƒtt	d| |t tƒt fƒ ƒ“d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sýJ ‚t| ddtt tƒtƒksJ ‚d S )NÚall©ÚhintÚseparable_Integralé   r   Ú11st_homogeneous_coeff_subs_dep_div_indep_IntegralÚBernoulli_IntegralÚ1st_homogeneous_coeff_bestÚ	BernoulliÚnth_algebraicÚ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_indepéÿÿÿÿÚ1st_power_series)r9   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eqÚoutputÚsol1Ú_yÚ_u1Úexpectedr3   r3   r4   Útest_dsolve_all_hint5   s`   ÿþýüûúùø	÷
öõ&ôóò(ñð ê$r]   c                   C   sX   t tƒ tttƒ t¡tttƒƒ tdƒdid W d   ƒ d S 1 s%w   Y  d S )Nr:   ©Úics)r)   ÚNotImplementedErrorr   r.   rR   r   r   r3   r3   r3   r4   Útest_dsolve_ics[   s   
,"ÿra   c               
      sn  t tt ƒ t ¡ tt ƒ ‰ tˆ dd} tˆ ddd}tˆ dd}g d¢}g d¢}t|  ¡ ƒ|ks2J ‚| d tˆ tt ƒƒks?J ‚| d	 ttt ƒtt  ƒksNJ ‚tˆ d	dttt ƒtt  ƒks_J ‚| d
 dksgJ ‚| d dksoJ ‚| d  	t
¡rxJ ‚| d  	t
¡rJ ‚| d  	t
¡rŠJ ‚| d  	t
¡r“J ‚| d  	t
¡rœJ ‚| d  	t
¡r¥J ‚| d  	t
¡s®J ‚| d  	t
¡s·J ‚| d  	t
¡sÀJ ‚| d  	t
¡sÉJ ‚| d  	t
¡sÒJ ‚t| ¡ ƒ|ksÜJ ‚|d tˆ tt ƒƒkséJ ‚|d	 ttt ƒtt  ƒksøJ ‚tˆ d	ddttt ƒtt  ƒksJ ‚|d
 dksJ ‚|d dksJ ‚| d |d ks(J ‚| d |d ks3J ‚| d |d ks>J ‚|d  	t
¡rHJ ‚|d  	t
¡rRJ ‚|d  	t
¡r\J ‚|d  	t
¡rfJ ‚|d  	t
¡rpJ ‚|d  	t
¡rzJ ‚|d  	t
¡s„J ‚|d  	t
¡sŽJ ‚|d  	t
¡s˜J ‚|d  	t
¡s¢J ‚|d  	t
¡s¬J ‚t| ¡ ƒ|ks·J ‚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sôJ ‚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s5J ‚d S )Nr6   r7   F)r8   ÚsimplifyÚall_Integral)rG   rH   r=   rJ   r;   rC   rM   rE   rF   r>   r<   Úalmost_linearÚalmost_linear_IntegralrN   rO   rP   Ú
factorablerI   r@   rQ   rB   r9   )rH   r;   rM   rF   r<   re   rN   rO   rP   rf   r@   rQ   r9   rQ   rN   rP   rf   rO   rG   rB   r=   rJ   rC   rE   rF   rH   r;   rM   r9   c                      ó   t ˆ ddS )NÚnotarealhintr7   ©r   r3   ©rW   r3   r4   Ú<lambda>Ÿ   ó    z%test_dsolve_options.<locals>.<lambda>c                      rg   )NÚ	Liouviller7   ri   r3   rj   r3   r4   rk       rl   r:   é   )rR   r.   r   r   ÚsortedÚkeysr'   r
   rV   Úhasr   r)   r2   r   r   )ÚaÚbÚcrp   ÚIntegral_keysr3   rj   r4   Útest_dsolve_optionsa   s€   
"&
ÿ
ÿ($
ÿ.ÿÿÿÿþrv   c                  C   s’  t ttƒ td¡ttƒƒdksJ ‚t ttƒttƒƒdksJ ‚t tttƒ t¡dƒttƒƒdks1J ‚t ttƒ t¡d ttƒƒdksCJ ‚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s˜J ‚|dksžJ ‚|dks¤J ‚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sÊJ ‚dt dttƒ t¡ ttƒd  ttƒt  dtd   ttƒƒv sîJ ‚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sEJ ‚d}t tttƒt tƒtttƒtƒ ƒ|ks^J ‚t tttƒt tƒtttƒtƒ ttƒdd|kszJ ‚t tdtd  ttƒ t¡ dƒttƒƒdks”J ‚t tdttƒd  ttƒ t¡ dƒttƒƒdks°J ‚t ttttƒtƒttƒt  dƒttƒƒdksÊJ ‚t
t tttƒdƒttƒddtƒsÞJ ‚tt tttƒ t¡dƒttƒdd ¡ ƒg d¢ksúJ ‚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g d¢ks,J ‚t ttƒ t¡tttƒt ƒ ttƒƒ} | dksGJ ‚d S )Nrn   )r?   rA   r@   rm   Ú2nd_power_series_ordinaryrD   ÚLiouville_Integral)r?   rD   r   )r?   rB   rG   rE   r>   r=   rC   rJ   rL   rI   rA   r@   rD   r9   rH   rF   r<   rM   r;   )rf   r?   rB   rG   rE   r>   r=   rC   rJ   rL   rI   r@   rD   r9   rH   rF   r<   rM   r;   )rG   rE   r>   rd   rL   rI   Ú3nth_linear_constant_coeff_undetermined_coefficientsÚ1nth_linear_constant_coeff_variation_of_parametersrH   rF   r<   re   Ú:nth_linear_constant_coeff_variation_of_parameters_Integral)
rf   rE   r>   rL   rI   ry   rz   rF   r<   r{   r:   )rf   rG   r>   rd   rI   rH   r<   re   Ú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   rk     s
    ÿÿz#test_classify_ode.<locals>.<lambda>Úk)rf   rB   rG   rE   r>   rL   rI   r9   rH   rF   r<   )rf   r?   rB   rG   rE   r>   r=   rC   rJ   rL   rI   ry   Ú<nth_linear_euler_eq_nonhomogeneous_undetermined_coefficientsrz   Ú:nth_linear_euler_eq_nonhomogeneous_variation_of_parametersrD   r9   rH   rF   r<   rM   r;   r{   ÚCnth_linear_euler_eq_nonhomogeneous_variation_of_parameters_IntegralT)Úprep)rf   r?   rB   rG   rE   r>   rL   rI   r@   rD   r9   rH   rF   r<   )rf   r?   rB   rG   rE   r>   rL   rI   rD   r9   rH   rF   r<   )rL   rI   é   ©Údict)rP   rA   rQ   r>   ©r‡   r8   )r>   r<   rP   rQ   Úordered_hints)rB   rG   rL   rI   r9   rH   )r   r.   rR   r   r
   r   r)   r2   r   ÚzÚ
isinstancer‡   ro   rp   )rr   rs   rt   r€   Úansr3   r3   r4   Útest_classify_ode©   sr   ÿ
&$&<<
>ÿþ>ÿ>ÿ,ÿÿÿ
þ.&ÿ
ÿ(
ÿ,
ÿ(
ÿ((
ÿJ(r   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                      ó   t ˆ ttƒˆdS ©Nr^   ©r   r.   rR   r3   ©rW   r_   r3   r4   rk   N  ó    z'test_classify_ode_ics.<locals>.<lambda>r   c                      rŽ   r   r   r3   r‘   r3   r4   rk   X  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   \  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   `  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   d  r’   r^   c                      rŽ   r   r   r3   r‘   r3   r4   rk   u  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   y  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   }  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk     r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   …  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   ‰  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   ™  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk     r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   ¡  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   ¥  r’   c                      rŽ   r   r   r3   r‘   r3   r4   rk   ©  r’   )r.   rR   r   r)   r2   r/   r   Úsubsr   r   rŠ   r3   r3   r‘   r4   Útest_classify_ode_icsH  sZ   	,r”   c            *      C   sL  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sùJ ‚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sšJ ‚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s_J ‚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sñJ ‚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s¤J ‚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trn   r   r:   Útype2F)Úno_of_equationÚ
func_coeffÚtype_of_equationÚfuncÚ	is_linearrW   rQ   rK   Útype3Útype4)r   rž   rœ   rW   r›   rQ   rš   r}   r…   Útype1)r   r   r   r
   r   r   r    r   )*r€   ÚlÚmÚnÚk1Úk2Úk3Úl1Úl2Úl3Úm1Úm2Úm3ÚPÚQÚRÚpÚqÚrÚP1ÚP2ÚP3ÚQ1ÚQ2ÚR1ÚR2rR   r   rŠ   r˜   Úx1Úy1Úeq6Úsol6Úeq7Úsol7Úeq8Úsol8Úeq11Úsol11Úeq13Úsol13r3   r3   r4   Útest_classify_sysode³  s„   L:8ÿHÿ
ÿÿý8:HÿJÿýdfÿ88ÿý,6Fÿ4ÿý@>Xÿ.ÿ&ÿýrÇ   c                  C   sÊ	  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s'J ‚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sHJ ‚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spJ ‚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s¡J ‚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sîJ ‚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s(J ‚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s\J ‚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sŸJ ‚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sÇJ ‚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sçJ ‚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sJ ‚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sJJ ‚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sqJ ‚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s°J ‚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säJ ‚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s4J ‚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soJ ‚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sªJ ‚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rhtdtdt|d | d|  t| | d
|  ikskJ ‚ J ‚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•J ‚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sãJ ‚d S )Nr:   rn   r^   r   rG   F)r_   r8   rb   r}   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   rk     s   H 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 )Nrn   r   )r$   r
   r.   rR   r   rV   r   r“   r3   r3   r3   r4   rk     s   D zEI q Lé   é   )r   r.   rR   r   r
   r   r   r“   r   r   r/   r   ÚHalfr   r$   rV   rÉ   r	   Úsetr   r)   r2   ÚC3ÚC4r   )rW   ÚKr³   Úf0ÚsolÚEIr²   ÚLÚsolsÚfuncsÚ	constantsÚics1Úics2Úsolved_constants1Úsolved_constants2r_   r3   r3   r4   Útest_solve_icsâ  sÀ   .ÿBP&ÿÿ< ÿ2ÿ ÿÿ.ÿÿ6
ÿ*
ÿ
ÿ*
ÿ@2ÿ

ÿ2 ÿ

ÿ>
ÿJ*
ÿ4*
ÿFLJ"
ÿJ"
ÿD
ýýüD8$6ÿrÜ   c                  C   sR  t dƒ} t dƒ}tdƒ}td| t| |ƒƒ | |ƒƒdksJ ‚t|t| |ƒ|ƒ d| | |ƒ  t|ƒ|  | |ƒƒdks?J ‚t|d | |ƒ ||¡ |t| |ƒ|ƒ  | |ƒ | |ƒƒdksaJ ‚tt|t| |ƒƒ ||ƒ| |ƒƒdksvJ ‚tt|t|t| |ƒƒ ||ƒ |ƒ| |ƒƒdksJ ‚tt| |ƒ||ƒ||ƒƒdks¡J ‚tt| |ƒ||ƒt||ƒ|ƒ | |ƒƒdks¹J ‚tt| |ƒ||ƒt||ƒ|ƒ ||ƒƒdksÑJ ‚tt|t|t| |ƒƒ ||ƒ |ƒ||ƒƒdksëJ ‚tt|| |ƒ |ƒ| |ƒƒdksýJ ‚t|tt|| |ƒd  ||ƒƒ | |ƒƒdksJ ‚tt|t|t| |ƒƒ ||ƒ |ƒ||ƒƒdks2J ‚tt| |ƒ||ƒ||ƒƒdksDJ ‚tt|t| |ƒƒ ||ƒ| |ƒƒdksZJ ‚tt| |ƒ||ƒt||ƒ|ƒ ||ƒƒdkssJ ‚tt|t| |ƒ||ƒ |ƒ| |ƒƒdksŠJ ‚t|tt|t| |ƒ|ƒd  ||ƒƒ | |ƒƒdks§J ‚d S )Nr.   r/   rR   r}   r   r:   rn   )r   r   r'   r   r   r   r   )r.   r/   rR   r3   r3   r4   Útest_ode_order=  s0   &@D*4"004$46$,2.*ÿÿrÝ   c                  C   sZ  t ttt ƒttt ƒ ttƒdksJ ‚t td ttƒttƒ  ttƒd u s(J ‚t tt tttt ƒ  ttƒdks<J ‚t tt ttd td  ƒ td ttƒttƒ   t	tt
ddƒ  ttƒd   ttƒt
ddƒkspJ ‚t tt ttt ƒ tt ttt ƒ  ttt ƒ ttƒdks’J ‚t ttƒtttƒƒdks J ‚t ttƒd tttƒƒdks°J ‚t tt t ttƒdks¾J ‚t tt t tttƒdksÍJ ‚t td ttƒ ttd ttƒd  ƒ ttƒƒd u sêJ ‚t tttƒd ttttƒtƒdksýJ ‚t tttƒd tttƒtƒd u sJ ‚t tttƒd ttttƒƒd u s#J ‚t tttƒd tttttƒƒd u s7J ‚t ttƒttƒtƒd u sFJ ‚t ttƒ t dtttƒt ƒ  ttƒtƒdksbJ ‚t tdt ƒttd ƒ ttƒd u swJ ‚t tdt ƒttƒ ttƒdksŠJ ‚t ttt ƒttƒdks™J ‚t dtdt ƒ dttƒ  ttƒdks°J ‚tdƒ} t | tdt ƒ | ttƒ  ttƒdksËJ ‚t ttƒ t¡ttƒd u sÛJ ‚t ttƒ t¡ t ttƒd u sîJ ‚t ttƒttƒd u sûJ ‚t tttd ƒ ttƒd u sJ ‚t tt	 tƒt	ksJ ‚t tt tƒd u s$J ‚ttd	d
„ ƒ d S )Nr   rn   r:   rÊ   r}   rK   rÈ   rr   c                   S   s   t tt ƒS r1   )r   rR   r   r3   r3   r3   r4   rk   u  rl   z(test_homogeneous_order.<locals>.<lambda>)r   r   r   rR   r   r   r   r   r   r	   r   r.   rŠ   r   r   r   r)   r2   )rr   r3   r3   r4   Útest_homogeneous_orderW  sF   (((4ÿÿÿD :&&&(8*&.. &"rÞ   c                  C   s>   t dt ƒ} t| ƒt| ƒ}}| t¡r| t¡rJ ‚d S d S )Nr:   )r   rR   r   r   rq   r   )r   Úir³   r3   r3   r4   Ú)test_noncircularized_real_imaginary_partsx  s    rà   c                  C   s.   dt td ƒ } | t| t td ƒƒksJ ‚d S )Nr:   rn   r}   )r   rR   r   )rÒ   r3   r3   r4   Ú$test_collect_respecting_exponentials‚  s   rá   c                  C   sx  t ttƒtƒddiksJ ‚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s3J ‚t ttƒttƒ tƒddiksDJ ‚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szJ ‚t ttƒtd  ttƒt  ttƒ tƒd| dœks–J ‚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sôJ ‚t dttƒ tƒddiksJ ‚t ttƒtƒddiksJ ‚t dt td t d  tƒddt tdt  td dt  hdœks8J ‚t tt tƒddiksFJ ‚t ttƒtdt d ƒ tƒdtddt  ƒhdœksdJ ‚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s™J ‚t ttƒtttƒ  tƒddiks­J ‚t ttƒttdt ƒ  tƒddiksÃJ ‚t ttƒt	tƒ tƒddiksÕJ ‚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=J ‚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sjJ ‚t dt t tƒddt tdt  hdœksƒJ ‚t dt tdt ƒ tƒddt tdt ƒ hdœks¡J ‚t tt ƒt tƒddiks²J ‚t t
d	ƒtƒdt
jhdœksÃJ ‚t dttƒ tƒdttƒhdœks×J ‚t ttt ƒtƒdttt ƒhdœksíJ ‚t ttƒtƒdttƒttƒhdœksJ ‚t ttƒtƒdttƒttƒhdœksJ ‚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s;J ‚t td tƒdt
jttd hdœksPJ ‚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stJ ‚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sJ ‚t tttƒ tƒdt
jtttƒttƒhdœks·J ‚t td dt  tƒdt
jttd hdœksÐJ ‚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sóJ ‚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J ‚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sDJ ‚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sqJ ‚t tdt ƒtd  tƒdt
jttd tdt ƒhdœks‘J ‚t ttt ƒ tƒdttt ƒ tt ƒhdœks­J ‚t ttdt ƒ tƒdt
jttdt ƒhdœksÈJ ‚t ttƒtt ƒ tƒdttƒttƒtt ƒhdœksæJ ‚t ttƒtƒdttƒhdœksøJ ‚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sJ ‚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sQJ ‚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sqJ ‚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sšJ ‚t ttd ƒtƒddiksªJ ‚t dtd  tƒddiksºJ ‚d S )NÚtestFrn   r…   T)râ   Útrialsetr:   r}   rÊ   )rã   râ   é   é   rÈ   é	   r~   )r%   r/   rR   r   r   r   r   r   r   r   r   ÚOner   rÌ   )Úsr3   r3   r4   Ú$test_undetermined_coefficients_match‰  s2  &ÿÿÿ@ÿ$ÿÿ$ÿ.Bþÿþ &
ÿ
ÿ$ÿ
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ÿ
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ÿÿ
þ
ÿ (
ÿ $ré   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/J ‚td ttƒd  ttƒ t¡ dt ttƒ  }t|ttƒƒdksSJ ‚d S )Nr   )ÚArn   )rf   rG   rE   r>   rd   rL   rI   ry   rz   rH   rF   r<   re   r{   )
rf   rG   r=   rC   rJ   rL   rI   rH   rM   r;   )Ú	sympy.abcrê   rR   r   r.   r   )rê   rW   r3   r3   r4   Útest_issue_4785_22462ø  s
   <2rì   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s%J ‚t tdd„ ƒ tttƒ t¡ttƒdddd ddœksBJ ‚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   r   r   r3   r3   r3   r4   rk     ó   ( 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   r   r3   r3   r3   r4   rk     s    )r)   r2   r   r.   rR   r   r   r3   r3   r3   r4   Útest_issue_4825  s   *
ÿ
ÿrî   c                  C   s¨   ddl m}  ttt tt  ƒttt tt  ƒ  kr'tt tt  ks*J ‚ J ‚ttt  tt  }| tttgdƒD ]\}}}t||t  |t  ƒ|ksQJ ‚q<d S )Nr   )Ú
variationsr}   )Úsympy.utilities.iterablesrï   r!   rV   rR   rÉ   r   rÎ   )rï   Úerr   rs   rt   r3   r3   r4   Ú'test_constant_renumber_order_issue_5308  s   ÿþ"ÿrò   c                  C   sâ   t dƒ\} }}}|| | | ||  g}t|d ƒ|| ks J ‚t|d |gdt| ks/J ‚t|d |gtgdt| ks@J ‚t|||gdt| t| t|  gksVJ ‚t|||gt dƒdt| t| t|  gksoJ ‚d S )Nze1:3 x yr   )Ú	variables)ró   ÚnewconstantszC3:5)r   r!   rV   rÉ   rÎ   rÏ   )Úe1Úe2rR   r   Úexprsr3   r3   r4   Útest_constant_renumber#  s   ",6rø   c                  C   sf  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s1J ‚tttt	ƒ t
tt	ƒ  tt	ƒ tt
hƒttt	ƒ tt	ƒ ksRJ ‚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sxJ ‚tttt	 ƒthƒttt	ƒ ksŠJ ‚tt	t t tthƒtt	 ks›J ‚tt	t tt	t	d	d
fƒ thƒtt	 ks±J ‚d S )Nr€   Tr,   r˜   ÚwrÈ   c                 S   s   g | ]
}|j  d ¡r|‘qS )ÚC)ÚnameÚ
startswith)Ú.0rè   r3   r3   r4   Ú
<listcomp>3  s    z#test_issue_5770.<locals>.<listcomp>r:   rn   )r   r   r   r   ÚlenÚfree_symbolsr"   rV   r   rR   rÉ   r   rÎ   r   r   r   )r€   r˜   rù   rÒ   r3   r3   r4   Útest_issue_5770.  s   *(ÿ.ÿ$"0r  c                   C   s@   t ttƒ ttƒ tƒd u sJ ‚t tttƒ ttƒd u sJ ‚d S r1   )r   r   rR   r   r   r3   r3   r3   r4   Útest_issue_5112_5430=  s     r  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 )Nrn   Úfdsjf)r   rR   r   r3   ©r.   r3   r4   rk   D  s    z!test_issue_5095.<locals>.<lambda>)r   r)   r2   r3   r3   r  r4   Útest_issue_5095B  s   r  c                  C   s®  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sJ ‚t|t| tƒƒdks™J ‚t|t| tƒƒd ks¥J ‚t|t| tƒƒdks±J ‚t|t| tƒƒdks½J ‚t|t| tƒƒdksÉJ ‚t|t| tƒƒd ksÕJ ‚d S )Nr.   r}   rÊ   r…   é   rn   r   )	r   r   rR   r   r   r   r   r   r   )r.   Úeq1Úeq2Úeq3Úeq4Úeq5r½   r¿   r3   r3   r4   Útest_homogeneous_functionG  s   , L r  c                  C   sÜ  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sRJ ‚| 	|ttƒ¡|	ks^J ‚| 	|ttƒ¡|	ksjJ ‚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 u sÈJ ‚| 	|ttƒ¡d u sÔJ ‚| 	|ttƒ¡d u sàJ ‚| 	|ttƒ¡d u sìJ ‚d S )
Nrn   r}   r…   r  ræ   é   rÊ   ióÿÿÿr:   )rŠ   rR   r.   r   r   Úexpandr&   r   r   Ú_linear_coeff_matchr   )r¤   ÚdÚratr  Úobj1r  Úobj2r	  Úobj3rŒ   r
  Úobj4r  Úobj5r½   Úobj6r¿   Úobj7r3   r3   r4   Útest_linear_coeff_matchY  s0   :04r  c                  C   s>   t tƒd } tttt tƒ|  | t  tgƒƒjƒdksJ ‚d S )Nrn   )r   rV   rÿ   r   r"   rR   Úgens)rt   r3   r3   r4   Útest_constantsimp_take_problemy  s   2r  c                  C   s´  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sJJ ‚t||ddd sUJ ‚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‰J ‚t||ddd s”J ‚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sØJ ‚d S )NrV   rn   r}   rÈ   rÊ   rË   r…   éx   rL   r7   r:   )rQ   r   rå   )r8   r_   r¤   )
r   r.   rR   r   r
   r   r   r   r   r   )rV   rW   rÒ   r3   r3   r4   Útest_series~  s    Bÿ
ÿ:J$r  c                  C   s,  t dƒ\} }ttƒ td¡tttƒ  }t|ƒdksJ ‚tttƒ|td d d  | t td d d   ttd ƒ ƒ}t|dd	|ksGJ ‚t||ƒd
ksPJ ‚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s˜J ‚tttƒ|t |  ttd ƒ ƒ}t|ddd|ks´J ‚t||ƒd
ks½J ‚dtd  ttƒ td¡ dt ttƒ t¡  dttƒ  }t|ƒdksäJ ‚tttƒ|td  d td  d  | t  ttd ƒ ƒ}t|dd	|ksJ ‚t||ƒd
ksJ ‚ttƒ td¡tttƒ t¡  ttƒ }t|ƒdks5J ‚tttƒ|td d td d  d  | t td  d d   ttd ƒ ƒ}t|ƒ|ksfJ ‚ttƒ td¡ttƒ t¡ tttƒ  }t|ƒdks„J ‚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¿J ‚ttƒ td¡tttƒ  }t|ƒdksÖJ ‚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
J ‚t||ƒd
ksJ ‚d S )NzC1 C2rn   )Ú2nd_linear_airyrw   r}   rÈ   r:   rä   rw   r7   ©Tr   rÊ   r~   )r8   Úx0)r8   r¤   )rf   Ú2nd_hypergeometricÚ2nd_hypergeometric_Integralrw   )rf   rw   rå   )rw   rË   é´   r  )
r   r.   rR   r   r   r
   r   r   r   r   )rV   rÉ   rW   rÒ   r3   r3   r4   Útest_2nd_power_series_ordinary’  sJ   B:.ÿ
þ"><*P*(*ÿ
ÿPr$  c                  C   s  t dƒ\} }}td ttƒ td¡ dt ttƒ t¡  dt d ttƒ  }tttƒ| td  dtd  d dtd   dt  d  ttd ƒ ƒ}t|d	d
|ksWJ ‚t||ƒdks`J ‚dtd  ttƒ td¡ dtd  ttƒ t¡  dtd  d ttƒ  }tttƒ| ttƒ td d td d  td d  t d  ttd ƒ ƒ}t|d	d
|ks¸J ‚t||ƒdksÁJ ‚td ttƒ td¡ td ttƒ t¡  td d ttƒ  }tttƒ| td  d dtd  d  td d  td d  td  d  t |td  td  d td d  td  d   ttd ƒ ƒ}t|ƒ|ks4J ‚t||ƒdks>J ‚td ttƒ td¡ tttƒ t¡  td t	ddƒ ttƒ  }tttƒ| td d td d  d  ttƒ |ttƒ td d td d  d   ttd ƒ ƒ}t|d	d
|ksžJ ‚t||ƒdks¨J ‚tttƒ td¡ ttƒ t¡ |t ttƒ  }tttƒ| |d td  d |td  d  d  ttd ƒ ƒ}t|ttƒd	d
|ksðJ ‚t||ƒdksúJ ‚ttƒ td¡dt t ttƒ t¡  |t ttƒ  }tttƒ| | td  |d  |d  |d  |d  d |td  |d  |d  |d  d  |td  |d  |d  d  |td  |d  d  |t  d  ttd ƒ ƒ}t|ttƒd	d
|ksJ ‚t||ƒdks‹J ‚d S )NzC1 C2 arn   r}   rÊ   iðÿÿÿræ   r:   rÈ   Ú2nd_power_series_regularr7   r  rå   rË   iÐ  r…   éP   é<   é   r  é@   i@8  i@  é$   )
r   rR   r.   r   r
   r   r   r   r   r   )rV   rÉ   rr   rW   rÒ   r3   r3   r4   Útest_2nd_power_series_regularÅ  sf   BJ>ÿÿN,ÿP0ÿ
ÿD.&ÿ
ÿ2B::&ÿÿþþþ
þr+  c                  C   s4   t dƒ} t dƒ}tt dƒtdƒ| ƒ ƒ|ksJ ‚d S )Nr˜   rÎ   rV   rÉ   )r   r#   r   )r˜   rÎ   r3   r3   r4   Útest_issue_15056ì  s   $r,  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sCJ ‚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skJ ‚d S )Nrn   r  )
rV   rR   r.   r   rÉ   r   r   r   r   r   ©rW   rÒ   r3   r3   r4   Útest_issue_15913ò  s   0D"r.  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   rk   ü  s   4 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   rk   ý  rí   )r)   r2   r3   r3   r3   r4   Útest_issue_16146û  s   r/  c                  C   sö   t tƒd t tƒ t¡ } tt tƒtƒ}t| ƒ|ksJ ‚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sJJ ‚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syJ ‚d S )Nrn   r:   r}   )
r.   rR   r   r
   rV   r   r   rÉ   rÍ   rÎ   r-  r3   r3   r4   Ú&test_dsolve_remove_redundant_solutions   s    (,"r0  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s=J ‚d S )NzA Br–   r˜   Tr   )r   r   r   r
   r   r   r   )rê   ÚBr˜   rW   rÒ   r3   r3   r4   Útest_issue_13060  s
   @r2  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sHJ ‚t dƒ\}}t|d
d}t|ƒttdƒƒks`J ‚d S )NzN sÚrhog      @r:   rÊ   rn   Tr6   rˆ   rw   Ú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   r   r+   Ústr)ÚNrè   r3  ÚeqnÚmatchrV   rÉ   rÒ   r3   r3   r4   Útest_issue_22523  s   Dÿr9  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sÑJ ‚|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J ‚d S )Nzx1, x2r–   zt k1 k2 m1 m2Tr,   )r:   r:   r:   r:   rn   r   r:   r^   r}   r…   é
   r(  éûÿÿÿ)r   r   r
   r   r   r“   r   r   )r»   Úx2r˜   r¥   r¦   r«   r¬   r  r  ÚeqsÚx1solÚx2solr3   r3   r4   Útest_issue_22604-  s   :..ÿTJÿ€r@  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v s=J ‚q0d S )	Niìÿÿÿrn   iô  i   r~   r…   r  r>   )r
   r.   rR   r   r   )Úder3   r3   r4   Útest_issue_22462;  s
   ..þýrB  c                  C   sP   t dƒ} tdƒ}tt|   || ƒ ¡  ¡  || ƒ ¡  dƒ}t|ƒdks&J ‚d S )NrR   r   r   )rm   Únth_order_reduciblerw   rx   )r   r   r
   r   r   r   )rR   r   rW   r3   r3   r4   Útest_issue_23425B  s   ,ÿrD  N)uÚsympy.core.functionr   r   r   r   Úsympy.core.numbersr   r   r   r	   Úsympy.core.relationalr
   Úsympy.core.singletonr   Úsympy.core.symbolr   r   Ú$sympy.functions.elementary.complexesr   r   Ú&sympy.functions.elementary.exponentialr   r   Ú%sympy.functions.elementary.hyperbolicr   Ú(sympy.functions.elementary.miscellaneousr   Ú(sympy.functions.elementary.trigonometricr   r   r   r   Úsympy.integrals.integralsr   Úsympy.polys.polytoolsr   Úsympy.series.orderr   Úsympy.simplify.radsimpr   Úsympy.solvers.oder   r   r   Úsympy.solvers.ode.subscheckr   Úsympy.solvers.ode.oder    r!   r"   r#   r$   Ú sympy.solvers.ode.nonhomogeneousr%   Úsympy.solvers.ode.singler&   Úsympy.solvers.deutilsr'   Úsympy.testing.pytestr(   r)   r*   Úsympy.utilities.miscr+   ÚC0rV   rÉ   rÎ   rÏ   ÚC5ÚC6ÚC7ÚC8ÚC9ÚC10ÚurR   r   rŠ   r.   r/   r0   r5   r]   ra   rv   r   r”   rÇ   rÜ   rÝ   rÞ   rà   rá   ré   rì   rî   rò   rø   r  r  r  r  r  r  r  r$  r+  r,  r.  r/  r0  r2  r9  r@  rB  rD  r3   r3   r3   r4   Ú<module>   s„    &
G  k/[!
	o
 
2'	