o
    à8Va€­  ã                   @   s2  d dl mZmZmZmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ d dlmZmZ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' d dl(m)Z) d dl*m+Z+ d dl,m-Z-m.Z.m/Z/ ed	ƒ\Z0Z1Z2Z3Z4Z5Z6Z7Z8Z9Z:ed
dd\Z;Z<Z=Z>edƒZ?edƒZ@edƒZAdd„ ZBdd„ ZCdd„ ZDe/dd„ ƒZEdd„ ZFdd„ ZGdd„ ZHdd„ ZId d!„ ZJd"d#„ ZKe-d$d%„ ƒZLd&d'„ ZMd(d)„ ZNd*d+„ ZOd,d-„ ZPd.d/„ ZQd0d1„ ZRd2d3„ ZSd4d5„ ZTd6d7„ ZUd8d9„ ZVd:d;„ ZWd<d=„ ZXd>d?„ ZYe/d@dA„ ƒZZdBdC„ Z[dDdE„ Z\dFdG„ Z]dHdI„ Z^dJdK„ Z_dLdM„ Z`dNS )Oé    )ÚacoshÚcosÚ
DerivativeÚdiffÚEqÚexpÚFunctionÚIÚIntegralÚlogÚOÚpiÚRationalÚSÚsinÚsqrtÚSubsÚSymbolÚtanÚsymbolsÚPolyÚreÚimÚatan2Ú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slowz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"   © r1   r1   úB/usr/lib/python3/dist-packages/sympy/solvers/ode/tests/test_ode.pyÚtest_get_numbered_constants%   s   

"ÿr3   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)r7   Ú11st_homogeneous_coeff_subs_indep_div_dep_IntegralÚbestÚ	best_hintÚdefaultÚorderrL   )r,   Úxr   r   ZlhsÚargsZrhsr   ÚC1r
   r   r   )ÚeqÚoutputZsol1Z_yZ_u1Zexpectedr1   r1   r2   Útest_dsolve_all_hint*   s`   ÿþýüûúùø	÷
öõ&ôóò(ñð ê$rU   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 )Nr8   ©Úics)r(   ÚNotImplementedErrorr   r,   rP   r   r   r1   r1   r1   r2   Útest_dsolve_icsP   s   
,"ÿrY   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 )Nr4   r5   F)r6   ÚsimplifyZall_Integral)rE   rF   r;   rH   r9   rA   rK   rC   rD   r<   r:   Úalmost_linearÚalmost_linear_IntegralrL   rM   rN   rG   r>   rO   r@   r7   )rF   r9   rK   rD   r:   r\   rL   rM   rN   r>   rO   r7   rO   rL   rN   r@   rM   rE   r;   rH   rA   rC   rD   rF   r9   rK   r7   c                      ó   t ˆ ddS )NZnotarealhintr5   ©r   r1   ©rS   r1   r2   Ú<lambda>”   ó    z%test_dsolve_options.<locals>.<lambda>c                      r]   )NÚ	Liouviller5   r^   r1   r_   r1   r2   r`   •   ra   r8   é   )rP   r,   r   r   ÚsortedÚkeysr&   r   rR   Úhasr
   r(   r0   r   r   )ÚaÚbÚcre   ZIntegral_keysr1   r_   r2   Útest_dsolve_optionsV   s€   
"&
ÿ
ÿ($
ÿ.ÿÿÿÿþrj   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 ‚d S )Nrc   )r=   r?   r>   rb   Ú2nd_power_series_ordinaryrB   ZLiouville_Integral)r=   rB   r   )r=   r@   rE   rC   r<   r;   rA   rH   rJ   rG   r?   r>   rB   r7   rF   rD   r:   rK   r9   )Ú
factorabler=   r@   rE   rC   r<   r;   rA   rH   rJ   rG   r>   rB   r7   rF   rD   r:   rK   r9   )rE   rC   r<   r[   rJ   rG   Ú3nth_linear_constant_coeff_undetermined_coefficientsÚ1nth_linear_constant_coeff_variation_of_parametersrF   rD   r:   r\   Ú:nth_linear_constant_coeff_variation_of_parameters_Integral)
rl   rC   r<   rJ   rG   rm   rn   rD   r:   ro   )	rC   r<   rJ   rG   rm   rn   rD   r:   ro   r8   )rE   r<   r[   rG   rF   r:   r\   ZRiccati_special_minus2é   éþÿÿÿc                   S   s&   t ttttƒ t¡ t¡ tttƒƒS r/   )r   rP   r,   Úyr   r1   r1   r1   r2   r`   ú   s
    ÿÿz#test_classify_ode.<locals>.<lambda>Úk)
r@   rE   rC   r<   rJ   rG   r7   rF   rD   r:   )r=   r@   rE   rC   r<   r;   rA   rH   rJ   rG   rm   Z<nth_linear_euler_eq_nonhomogeneous_undetermined_coefficientsrn   Z:nth_linear_euler_eq_nonhomogeneous_variation_of_parametersrB   r7   rF   rD   r:   rK   r9   ro   ZCnth_linear_euler_eq_nonhomogeneous_variation_of_parameters_IntegralT)Zprep)rl   r=   r@   rE   rC   r<   rJ   rG   r>   rB   r7   rF   rD   r:   )rl   r=   r@   rE   rC   r<   rJ   rG   rB   r7   rF   rD   r:   )rJ   rG   é   ©Údict)rN   r?   rO   r<   )rv   r6   )r<   r:   rN   rO   Úordered_hints)r   r,   rP   r   r   r   r(   r0   r   ÚzÚ
isinstancerv   rd   re   )rg   rh   ri   rs   Úansr1   r1   r2   Útest_classify_odež   sn   ÿ
&$&<<

>ÿþ>ÿ>ÿ,ÿÿÿ
þ.&ÿ
ÿ(
ÿ,
ÿ(
ÿ((
ÿJr{   c                      s>  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 dƒi‰tt‡ ‡fdd„ƒ 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 dƒi‰tt‡ ‡fdd„ƒ 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 dƒi‰tt‡ ‡fdd„ƒ t tƒ t¡ tt¡di‰tˆ t tƒˆd	 d S )Nr8   c                      ó   t ˆ ttƒˆdS ©NrV   ©r   r,   rP   r1   ©rS   rW   r1   r2   r`   ;  ó    z'test_classify_ode_ics.<locals>.<lambda>r   c                      r|   r}   r~   r1   r   r1   r2   r`   E  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   I  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   M  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   R  r€   rV   c                      r|   r}   r~   r1   r   r1   r2   r`   _  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   c  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   g  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   k  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   o  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   t  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   €  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   „  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   ˆ  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   Œ  r€   c                      r|   r}   r~   r1   r   r1   r2   r`   ‘  r€   )r,   rP   r   r(   r0   r-   r   Úsubsrr   r   rx   r1   r1   r   r2   Útest_classify_ode_ics5  sN   	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)Z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trc   r   r8   Ztype2F)Úno_of_equationÚ
func_coeffÚtype_of_equationÚfuncÚ	is_linearrS   rO   rI   Ztype3Ztype4)r‰   rŠ   rˆ   rS   r‡   rO   r†   rp   rt   Ztype1)r   r   r   r   r   r   r   r   )*rs   ÚlÚmÚnZk1Zk2Zk3Úl1Úl2Úl3Zm1Zm2Zm3ÚPÚQÚRÚpÚqÚrZP1ZP2ZP3ZQ1ZQ2ZR1ZR2rP   rr   rx   r…   Zx1Zy1Úeq6Zsol6Úeq7Zsol7Zeq8Zsol8Zeq11Zsol11Zeq13Zsol13r1   r1   r2   Útest_classify_sysode—  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r™   c                  C   sÚ  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 ‚d S )Nr8   rc   rV   r   rE   F)rW   r6   rZ   rp   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   r8   )	r#   r   r,   rP   rR   r   ÚC2r   r   r1   r1   r1   r2   r`   û  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 )Nrc   r   )r#   r   r,   rP   r   rR   r   r   r1   r1   r1   r2   r`   þ  s   D zEI q Lé   é   )r   r,   rP   r   r   r   r   r   r   r   r-   r   ÚHalfr   r#   rR   r›   r   Úsetr   r(   r0   ÚC3ÚC4r   )rS   ÚKr–   Zf0ÚsolZEIr•   ÚLZsolsZfuncsZ	constantsZics1Zics2Zsolved_constants1Zsolved_constants2r1   r1   r2   Útest_solve_icsÆ  s´   .ÿBP&ÿÿ< ÿ2ÿ ÿÿ.ÿÿ6
ÿ*
ÿ
ÿ*
ÿ@2ÿ

ÿ2 ÿ

ÿ>
ÿJ*
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ÿFLJ"
ÿJ"
ÿD
ýýür¥   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-   rP   rp   r   r8   rc   )r   r   r&   r   r   r   r   )r,   r-   rP   r1   r1   r2   Útest_ode_order  s0   &@D*4"004$46$,2.*ÿÿr¦   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$J ‚ttd	d
„ ƒ d S )Nr   rc   r8   rœ   rp   rI   rš   rg   c                   S   s   t tt ƒS r/   )r   rP   rr   r1   r1   r1   r2   r`   R  ra   z(test_homogeneous_order.<locals>.<lambda>)r   r   rr   rP   r   r   r   r   r   r   r   r,   rx   r   r   r   r(   r0   )rg   r1   r1   r2   Útest_homogeneous_order4  sF   (((4ÿÿÿD :&&&(8*&.. &"r§   c                  C   s>   t dt ƒ} t| ƒt| ƒ}}| t¡r| t¡rJ ‚d S d S )Nr8   )r   rP   r   r   rf   r   )rr   Úir–   r1   r1   r2   Ú)test_noncircularized_real_imaginary_partsU  s    r©   c                  C   s.   dt td ƒ } | t| t td ƒƒksJ ‚d S )Nr8   rc   rp   )r   rP   r   )r£   r1   r1   r2   Ú$test_collect_respecting_exponentials_  s   rª   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testFrc   rt   T)r«   Útrialsetr8   rp   rœ   )r¬   r«   é   é   rš   é	   rq   )r$   r-   rP   r   r   r   r   r   rr   r   r   ZOner	   rž   )Úsr1   r1   r2   Ú$test_undetermined_coefficients_matchf  s2  &ÿÿÿ@ÿ$ÿÿ$ÿ.Bþÿþ &
ÿ
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ÿÿ
þ
ÿ (
ÿ $r±   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Arc   )rE   rC   r[   rJ   rG   rm   rn   rF   rD   r\   ro   )	rE   r;   rA   rH   rJ   rG   rF   rK   r9   )Z	sympy.abcr²   rP   r   r,   r   )r²   rS   r1   r1   r2   Útest_issue_4785Ô  s
   <2r³   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 r/   )r   r,   rP   rr   r   r1   r1   r1   r2   r`   é  ó   ( z!test_issue_4825.<locals>.<lambda>Tru   r   r1   )rO   rN   rw   c                   S   s   t ttƒ t¡ttƒƒS r/   )r   r,   rP   r   rr   r1   r1   r1   r2   r`   í  s    )r(   r0   r   r,   rP   rr   r   r1   r1   r1   r2   Útest_issue_4825è  s   *
ÿ
ÿrµ   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
variationsrp   )Zsympy.utilities.iterablesr¶   r    rR   rP   r›   rr   r    )r¶   Úerg   rh   ri   r1   r1   r2   Ú'test_constant_renumber_order_issue_5308ò  s   ÿþ"ÿr¸   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)r¹   ZnewconstantszC3:5)r   r    rR   r›   r    r¡   )Ze1Ze2rP   rr   Zexprsr1   r1   r2   Útest_constant_renumberý  s   ",6rº   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 )Nrs   Tr*   r…   Úwrš   c                 S   s   g | ]
}|j  d ¡r|‘qS )ÚC)ÚnameÚ
startswith)Ú.0r°   r1   r1   r2   Ú
<listcomp>  s    z#test_issue_5770.<locals>.<listcomp>r8   rc   )r   r   r   r   ÚlenZfree_symbolsr!   rR   r   rP   r›   r   r    r   rr   r
   )rs   r…   r»   r£   r1   r1   r2   Útest_issue_5770  s   *(ÿ.ÿ$"0rÂ   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 r/   )r   r   rP   r   rr   r1   r1   r1   r2   Útest_issue_5112_5430  s     rÃ   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 )Nrc   Zfdsjf)r   rP   r   r1   ©r,   r1   r2   r`     s    z!test_issue_5095.<locals>.<lambda>)r   r(   r0   r1   r1   rÄ   r2   Útest_issue_5095  s   rÅ   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,   rp   rœ   rt   é   rc   r   )	r   r   rP   r   r   r   r   r   r   )r,   Úeq1Úeq2Úeq3Úeq4Úeq5r—   r˜   r1   r1   r2   Útest_homogeneous_function!  s   , L rÌ   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 )
Nrc   rp   rt   rÆ   r¯   é   rœ   ióÿÿÿr8   )rx   rP   r,   r   r   Úexpandr%   r   r   Z_linear_coeff_matchr   )r   ÚdZratrÇ   Zobj1rÈ   Zobj2rÉ   Zobj3rz   rÊ   Zobj4rË   Zobj5r—   Zobj6r˜   Zobj7r1   r1   r2   Útest_linear_coeff_match3  s0   :04rÐ   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 )Nrc   )r   rR   rÁ   r   r!   rP   Zgens)ri   r1   r1   r2   Útest_constantsimp_take_problemS  s   2rÑ   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 )NrR   rc   rp   rš   rœ   r   rt   éx   rJ   r5   r8   )rO   r   r®   )r6   rW   r   )
r   r,   rP   r   r   r   r   r   r   r   )rR   rS   r£   r1   r1   r2   Útest_seriesX  s    Bÿ
ÿ:J$rÓ   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 C2rc   )Z2nd_linear_airyrk   rp   rš   r8   r­   rk   r5   ©Tr   rœ   rq   )r6   Zx0)r6   r   )Z2nd_hypergeometricZ2nd_hypergeometric_Integralrk   )rk   r®   r   é´   rÆ   )
r   r,   rP   r   r   r   r   r   r   r   )rR   r›   rS   r£   r1   r1   r2   Útest_2nd_power_series_ordinaryl  sJ   B:.ÿ
þ"><*P*(*ÿ
ÿPrÖ   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 arc   rp   rœ   iðÿÿÿr¯   r8   rš   Z2nd_power_series_regularr5   rÔ   r®   r   iÐ  rt   éP   é<   é   rÒ   é@   i@8  i@  é$   )
r   rP   r,   r   r   r   r   r   r   r   )rR   r›   rg   rS   r£   r1   r1   r2   Útest_2nd_power_series_regularŸ  sf   BJ>ÿÿN,ÿP0ÿ
ÿD.&ÿ
ÿ2B::&ÿÿþþþ
þrÜ   c                  C   s4   t dƒ} t dƒ}tt dƒtdƒ| ƒ ƒ|ksJ ‚d S )Nr…   r    rR   r›   )r   r"   r   )r…   r    r1   r1   r2   Útest_issue_15056Æ  s   $rÝ   c                  C   sÚ   t  t dt ttƒ  ttƒ tttƒtƒ } tttd t ƒ ttd t ƒtt ttd  t ƒ t tƒ  }t| |ƒdksCJ ‚t ttt t ƒ  }ttttƒ tƒttƒ 	td¡ } t| |ttƒƒdkskJ ‚d S )Nrc   rÔ   )
rR   rP   r,   r   r›   r   r
   r   rr   r   ©rS   r£   r1   r1   r2   Útest_issue_15913Ì  s   0D"rß   c                   C   s    t tdd„ ƒ t tdd„ ƒ d S )Nc                   S   s4   t ttƒ t¡ttƒ t¡gttƒttƒttƒgƒS r/   )r   r,   rP   r   r-   r.   r1   r1   r1   r2   r`   Ö  s   4 z"test_issue_16146.<locals>.<lambda>c                   S   s(   t ttƒ t¡ttƒ t¡gttƒgƒS r/   )r   r,   rP   r   r-   r1   r1   r1   r2   r`   ×  r´   )r(   r0   r1   r1   r1   r2   Útest_issue_16146Õ  s   rà   c                  C   sö   t tƒd t tƒ t¡ } tt tƒtƒ}t| ƒ|ksJ ‚t tƒttƒ t tƒ td¡ } tt tƒttt  ƒtt tƒttƒƒh}tt| ƒƒ|ksJJ ‚t tƒd dt tƒ  d t tƒ td¡ } tt tƒttt  t	td   ƒ}t| ƒ|ksyJ ‚d S )Nrc   r8   rp   )
r,   rP   r   r   rR   r   r   r›   rŸ   r    rÞ   r1   r1   r2   Ú&test_dsolve_remove_redundant_solutionsÚ  s    (,"rá   c                  C   s~   t dtd\} }tdƒ}tt| |ƒ|ƒ| |ƒ||ƒ ƒtt||ƒ|ƒ| |ƒ||ƒ ƒg}t|ƒ}t||ƒdddgfks=J ‚d S )NzA Brƒ   r…   Tr   )r   r   r   r   r   r   r   )r²   ÚBr…   rS   r£   r1   r1   r2   Útest_issue_13060é  s
   @rã   N)aZsympyr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.solvers.oder   r   r   Zsympy.solvers.ode.subscheckr   Zsympy.solvers.ode.oder   r    r!   r"   r#   Z sympy.solvers.ode.nonhomogeneousr$   Zsympy.solvers.ode.singler%   Zsympy.solvers.deutilsr&   Zsympy.testing.pytestr'   r(   r)   ZC0rR   r›   r    r¡   ZC5ZC6ZC7ZC8ZC9ZC10ÚurP   rr   rx   r,   r-   r.   r3   rU   rY   rj   r{   r‚   r™   r¥   r¦   r§   r©   rª   r±   r³   rµ   r¸   rº   rÂ   rÃ   rÅ   rÌ   rÐ   rÑ   rÓ   rÖ   rÜ   rÝ   rß   rà   rá   rã   r1   r1   r1   r2   Ú<module>   s`   l &
G b/T!
	n
 
2'	