U
    —9%eÏM  ã                   @   s¼   d dl mZmZ d dlmZmZmZmZmZm	Z	m
Z
mZ dd„ Zdd„ Zdd„ Zd	d
„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd„ Zdd „ Zd!d"„ Zd#S )$é    )ÚSÚRational)Úgauss_legendreÚgauss_laguerreÚgauss_hermiteÚgauss_gen_laguerreÚgauss_chebyshev_tÚgauss_chebyshev_uÚgauss_jacobiÚgauss_lobattoc                  C   s  t ddƒ\} }dd„ | D ƒdgks&t‚dd„ |D ƒdgks>t‚t ddƒ\} }d	d„ | D ƒd
dgksft‚dd„ |D ƒddgks€t‚t ddƒ\} }dd„ | D ƒdddgksªt‚dd„ |D ƒdddgksÆt‚t ddƒ\} }dd„ | D ƒddddgksòt‚dd„ |D ƒddddgkst‚d S )Né   é   c                 S   s   g | ]}t |ƒ‘qS © ©Ústr©Ú.0Úrr   r   úd/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/integrals/tests/test_quadrature.pyÚ
<listcomp>
   s     z!test_legendre.<locals>.<listcomp>Ú0c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     ú2.0000000000000000é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     z-0.57735026918962576z0.57735026918962576c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     ú1.0000000000000000é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     z-0.77459666924148338z0.77459666924148338c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     z0.55555555555555556z0.88888888888888889é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r       s     z-0.86113631159405258z-0.33998104358485626z0.33998104358485626z0.86113631159405258c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   %   s     z0.34785484513745386z0.65214515486254614©r   ÚAssertionError©ÚxÚwr   r   r   Útest_legendre   sH    þ
þ
ý
ý
ü
ür!   c                  C   sJ   t ddƒ\} }dd„ | D ƒdddgks*t‚dd„ |D ƒd	d
d	gksFt‚d S )Nr   é(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   .   s     z)test_legendre_precise.<locals>.<listcomp>z+-0.7745966692414833770358530799564799221666r   z*0.7745966692414833770358530799564799221666c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   2   s     z*0.5555555555555555555555555555555555555556z*0.8888888888888888888888888888888888888889r   r   r   r   r   Útest_legendre_precise,   s    ý
ýr#   c                  C   sh  t ddƒ\} }dd„ | D ƒdgks&t‚dd„ |D ƒdgks>t‚t ddƒ\} }dd„ | D ƒd	d
gksft‚dd„ |D ƒddgks€t‚t ddƒ\} }dd„ | D ƒdddgksªt‚dd„ |D ƒdddgksÆt‚t ddƒ\} }dd„ | D ƒddddgksòt‚dd„ |D ƒddd d!gkst‚t d"dƒ\} }d#d„ | D ƒd$d%d&d'd(gksBt‚d)d„ |D ƒd*d+d,d-d.gksdt‚d S )/Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   :   s     z!test_laguerre.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ;   s     r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   >   s     z0.58578643762690495z3.4142135623730950c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   A   s     z0.85355339059327376z0.14644660940672624r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   F   s     z0.41577455678347908z2.2942803602790417z6.2899450829374792c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   K   s     z0.71109300992917302z0.27851773356924085z0.010389256501586136r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   R   s     z0.32254768961939231z1.7457611011583466z4.5366202969211280z9.3950709123011331c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   W   s     z0.60315410434163360z0.35741869243779969z0.038887908515005384z0.00053929470556132745é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ^   s     z0.26356031971814091z1.4134030591065168z3.5964257710407221z7.0858100058588376z12.640800844275783c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   d   s     z0.52175561058280865z0.39866681108317593z0.075942449681707595z0.0036117586799220485z2.3369972385776228e-5©r   r   r   r   r   r   Útest_laguerre8   sf    þ
þ
ý
ý
ü
üûûr&   c                  C   sJ   t ddƒ\} }dd„ | D ƒdddgks*t‚dd„ |D ƒd	d
dgksFt‚d S )Nr   r"   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   n   s     z)test_laguerre_precise.<locals>.<listcomp>z*0.4157745567834790833115338731282744735466z)2.294280360279041719822050361359593868960z)6.289945082937479196866415765512131657493c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   r   s     z*0.7110930099291730154495901911425944313094z*0.2785177335692408488014448884567264810349z+0.01038925650158613574896492040067908765572r%   r   r   r   r   Útest_laguerre_precisel   s    ý
ýr'   c                  C   sh  t ddƒ\} }dd„ | D ƒdgks&t‚dd„ |D ƒdgks>t‚t ddƒ\} }d	d„ | D ƒd
dgksft‚dd„ |D ƒddgks€t‚t ddƒ\} }dd„ | D ƒdddgksªt‚dd„ |D ƒdddgksÆt‚t ddƒ\} }dd„ | D ƒddddgksòt‚dd„ |D ƒddddgkst‚t ddƒ\} }dd„ | D ƒd d!dd"d#gksBt‚d$d„ |D ƒd%d&d'd&d%gksdt‚d S )(Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   z   s     z test_hermite.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   {   s     ú1.7724538509055160r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ~   s     ú-0.70710678118654752ú0.70710678118654752c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     z0.88622692545275801r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   †   s     z-1.2247448713915890z1.2247448713915890c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Š   s     z0.29540897515091934z1.1816359006036774r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     z-1.6506801238857846z-0.52464762327529032z0.52464762327529032z1.6506801238857846c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   •   s     z0.081312835447245177z0.80491409000551284r$   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   œ   s     z-2.0201828704560856z-0.95857246461381851z0.95857246461381851z2.0201828704560856c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¢   s     z0.019953242059045913z0.39361932315224116z0.94530872048294188©r   r   r   r   r   r   Útest_hermitex   sf    þ
þ
ý
ý
ü
üûûr,   c                  C   sJ   t ddƒ\} }dd„ | D ƒdddgks*t‚dd„ |D ƒd	d
d	gksFt‚d S )Nr   r"   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¬   s     z(test_hermite_precise.<locals>.<listcomp>z*-1.224744871391589049098642037352945695983r   z)1.224744871391589049098642037352945695983c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   °   s     z*0.2954089751509193378830279138901908637996z)1.181635900603677351532111655560763455198r+   r   r   r   r   Útest_hermite_preciseª   s    ý
ýr-   c                  C   s  t dtddƒdƒ\} }dd„ | D ƒdgks.t‚dd„ |D ƒd	gksFt‚t dtddƒdƒ\} }d
d„ | D ƒddgksvt‚dd„ |D ƒddgkst‚t dtddƒdƒ\} }dd„ | D ƒdddgksÂt‚dd„ |D ƒdddgksÞt‚t dtddƒdƒ\} }dd„ | D ƒddddgkst‚dd„ |D ƒd d!d"d#gks4t‚t d$tddƒdƒ\} }d%d„ | D ƒd&d'd(d)d*gkslt‚d+d„ |D ƒd,d-d.d/d0gksŽt‚t dddƒ\} }d1d„ | D ƒd2gks¸t‚d3d„ |D ƒd4gksÒt‚t dddƒ\} }d5d„ | D ƒd4d6gksþt‚d7d„ |D ƒd8dgkst‚t dddƒ\} }d9d„ | D ƒd:d;d<gksHt‚d=d„ |D ƒd>d?d@gksft‚t dddƒ\} }dAd„ | D ƒdBdCdDdEgks–t‚dFd„ |D ƒdGdHdIdJgks¶t‚t d$ddƒ\} }dKd„ | D ƒdLdMdNdOdPgksèt‚dQd„ |D ƒdRdSdTdUdVgks
t‚d S )WNr   éÿÿÿÿr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¸   s     z%test_gen_laguerre.<locals>.<listcomp>ú0.50000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¹   s     r(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¼   s     z0.27525512860841095z2.7247448713915890c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¿   s     z1.6098281800110257z0.16262567089449035r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ä   s     z0.19016350919348813z1.7844927485432516z5.5253437422632603c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   È   s     z1.4492591904487850z0.31413464064571329z0.0090600198110176913r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Î   s     z0.14530352150331709z1.3390972881263614z3.9269635013582872z8.5886356890120343c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ó   s     z1.3222940251164826z0.41560465162978376z0.034155966014826951z0.00039920814442273524r$   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ú   s     z0.11758132021177814z1.0745620124369040z3.0859374437175500z6.4147297336620305z11.807189489971737c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   à   s     z1.2217252674706516z0.48027722216462937z0.067748788910962126z0.0026872914935624654z1.5280865710465241e-5c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   è   s     z3.0000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   é   s     r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ì   s     z6.0000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ï   s     z1.5000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ô   s     z1.5173870806774125z4.3115831337195203z9.1710297856030672c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ø   s     z1.0374949614904253z0.90575000470306537z0.056755033806509347c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   þ   s     z1.2267632635003021z3.4125073586969460z6.9026926058516134z12.458036771951139c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z0.72552499769865438z1.0634242919791946z0.20669613102835355z0.0043545792937974889c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   
  s     z1.0311091440933816z2.8372128239538217z5.6202942725987079z9.6829098376640271z15.828473921690062c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z0.52091739683509184z1.0667059331592211z0.38354972366693113z0.028564233532974658z0.00026271280578124935©r   r   r   r   r   r   r   Útest_gen_laguerre¶   sÌ    þ
þ
ý
ý
üüûûþþýýüüûûr1   c                  C   sš   t dtddƒdƒ\} }dd„ | D ƒddd	gks2t‚d
d„ |D ƒdddgksNt‚t dddƒ\} }dd„ | D ƒdddgkszt‚dd„ |D ƒdddgks–t‚d S )Nr   r.   r   r"   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z-test_gen_laguerre_precise.<locals>.<listcomp>z*0.1901635091934881328718554276203028970878z)1.784492748543251591186722461957367638500z)5.525343742263260275941422110422329464413c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z)1.449259190448785048183829411195134343108z*0.3141346406457132878326231270167565378246z,0.009060019811017691281714945129254301865020c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   $  s     z)1.517387080677412495020323111016672547482z)4.311583133719520302881184669723530562299z)9.171029785603067202098492219259796890218c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   (  s     z)1.037494961490425285817554606541269153041z*0.9057500047030653669269785048806009945254z+0.05675503380650934725546688857812985243312r0   r   r   r   r   Útest_gen_laguerre_precise  s,    ý
ý
ý
ýr2   c                  C   sh  t ddƒ\} }dd„ | D ƒdgks&t‚dd„ |D ƒdgks>t‚t ddƒ\} }d	d„ | D ƒd
dgksft‚dd„ |D ƒddgks€t‚t ddƒ\} }dd„ | D ƒdddgksªt‚dd„ |D ƒdddgksÆt‚t ddƒ\} }dd„ | D ƒddddgksòt‚dd„ |D ƒddddgkst‚t ddƒ\} }dd„ | D ƒdddd d!gksBt‚d"d„ |D ƒd#d#d#d#d#gksdt‚d S )$Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   0  s     z$test_chebyshev_t.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   1  s     ú3.1415926535897932r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   4  s     r*   r)   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   7  s     ú1.5707963267948966r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   <  s     ú0.86602540378443865ú-0.86602540378443865c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   @  s     ú1.0471975511965977r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   F  s     z0.92387953251128676z0.38268343236508977z-0.38268343236508977z-0.92387953251128676c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   K  s     ú0.78539816339744831r$   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   R  s     z0.95105651629515357z0.58778525229247313z-0.58778525229247313z-0.95105651629515357c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   X  s     z0.62831853071795865©r   r   r   r   r   r   Útest_chebyshev_t.  sf    þ
þ
ý
ý
ü
üûûr:   c                  C   sJ   t ddƒ\} }dd„ | D ƒdddgks*t‚dd„ |D ƒd	d	d	gksFt‚d S )
Nr   r"   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   b  s     z,test_chebyshev_t_precise.<locals>.<listcomp>z*0.8660254037844386467637231707529361834714r   z+-0.8660254037844386467637231707529361834714c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   f  s     z)1.047197551196597746154214461093167628066r9   r   r   r   r   Útest_chebyshev_t_precise`  s    ý
ýr;   c                  C   sh  t ddƒ\} }dd„ | D ƒdgks&t‚dd„ |D ƒdgks>t‚t ddƒ\} }d	d„ | D ƒd
dgksft‚dd„ |D ƒddgks€t‚t ddƒ\} }dd„ | D ƒdddgksªt‚dd„ |D ƒdddgksÆt‚t ddƒ\} }dd„ | D ƒddddgksòt‚dd„ |D ƒddddgkst‚t ddƒ\} }dd„ | D ƒdd
ddd gksBt‚d!d„ |D ƒd"dd#dd"gksdt‚d S )$Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   n  s     z$test_chebyshev_u.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   o  s     r4   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   r  s     r/   z-0.50000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   u  s     r8   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   z  s     r*   r)   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ~  s     z0.39269908169872415r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   „  s     ú0.80901699437494742z0.30901699437494742ú-0.30901699437494742z-0.80901699437494742c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ‰  s     z0.21707871342270599z0.56831944997474231r$   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     r5   r6   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   –  s     z0.13089969389957472z0.52359877559829887©r	   r   r   r   r   r   Útest_chebyshev_ul  sf    þ
þ
ý
ý
ü
üûûr?   c                  C   sJ   t ddƒ\} }dd„ | D ƒdddgks*t‚dd„ |D ƒd	d
d	gksFt‚d S )Nr   r"   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      s     z,test_chebyshev_u_precise.<locals>.<listcomp>z*0.7071067811865475244008443621048490392848r   z+-0.7071067811865475244008443621048490392848c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¤  s     z*0.3926990816987241548078304229099378605246z*0.7853981633974483096156608458198757210493r>   r   r   r   r   Útest_chebyshev_u_precisež  s    ý
ýr@   c                  C   s,  t dtddƒtjdƒ\} }dd„ | D ƒdgks2t‚dd„ |D ƒd	gksJt‚t dtddƒtjdƒ\} }d
d„ | D ƒddgks~t‚dd„ |D ƒddgks˜t‚t dtddƒtjdƒ\} }dd„ | D ƒdddgksÎt‚dd„ |D ƒdddgksêt‚t dtddƒtjdƒ\} }dd„ | D ƒddddgks$t‚dd„ |D ƒdd d!d"gksDt‚t d#tddƒtjdƒ\} }d$d„ | D ƒd%d&d'd(d)gks€t‚d*d„ |D ƒd+d,d-d.d/gks¢t‚t ddddƒ\} }d0d„ | D ƒd1gksÎt‚d2d„ |D ƒd3gksèt‚t ddddƒ\} }d4d„ | D ƒd5d6gkst‚d7d„ |D ƒd8d9gks2t‚t ddddƒ\} }d:d„ | D ƒd;d<d=gksbt‚d>d„ |D ƒd?d@dAgks€t‚t ddddƒ\} }dBd„ | D ƒdCdDdEdFgks²t‚dGd„ |D ƒdHdIdJdKgksÒt‚t d#dddƒ\} }dLd„ | D ƒdMdNdOdPdQgkst‚dRd„ |D ƒdSdTdUdVdWgks(t‚d S )XNr   r.   r   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¬  s     ztest_jacobi.<locals>.<listcomp>r/   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ­  s     r3   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   °  s     r=   r<   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ³  s     z0.86831485369082398z2.2732777998989693r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¸  s     z-0.62348980185873353z0.22252093395631440z0.90096886790241913c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¼  s     z0.33795476356635433z1.0973322242791115z1.7063056657443274r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Â  s     z-0.76604444311897804z-0.17364817766693035z0.93969262078590838c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ç  s     z0.16333179083642836z0.57690240318269103r7   z1.3541609083740761r$   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Î  s     z-0.84125353283118117z-0.41541501300188643z0.14231483827328514z0.65486073394528506z0.95949297361449739c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ô  s     z0.090675770007435372z0.33391416373675607z0.65248870981926643z0.94525424081394926z1.1192597692123861c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ü  s     z0.14285714285714286c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ý  s     z1.0666666666666667c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   à  s     z-0.24025307335204215z0.46247529557426437c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ã  s     z0.48514624517838660z0.58152042148828007c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   è  s     z-0.46115870378089762z0.10438533038323902z0.62950064612493132c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ì  s     z0.17937613502213266z0.61595640991147154z0.27133412173306246c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ò  s     z-0.59903470850824782z-0.14761105199952565z0.32554377081188859z0.72879429738819258c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ÷  s     z0.067809641836772187z0.38956404952032481z0.47995970868024150z0.12933326662932816c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   þ  s     z-0.69045775012676106z-0.32651993134900065z0.082337849552034905z0.47517887061283164z0.79279429464422850c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z0.027410178066337099z0.21291786060364828z0.43908437944395081z0.32220656547221822z0.065047683080512268©r
   r   r   ZHalfr   r   r   r   r   Útest_jacobiª  sÌ    þ
þ
ý
ý
üüûûþþýýüüûûrB   c                  C   s    t dtddƒtjdƒ\} }dd„ | D ƒddd	gks6t‚d
d„ |D ƒdddgksRt‚t ddddƒ\} }dd„ | D ƒdddgks€t‚dd„ |D ƒdddgksœt‚d S )Nr   r.   r   r"   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z'test_jacobi_precise.<locals>.<listcomp>z+-0.6234898018587335305250048840042398106323z*0.2225209339563144042889025644967947594664z*0.9009688679024191262361023195074450511659c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z*0.3379547635663543330553835737094171534907z)1.097332224279111467485302294320899710461z)1.706305665744327437921957515249186020246c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z+-0.4611587037808976179121958105554375981274z*0.1043853303832390210914918407615869143233z*0.6295006461249313240934312425211234110769c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     s     z*0.1793761350221326596137764371503859752628z*0.6159564099114715430909548532229749439714z*0.2713341217330624639619353762933057474325rA   r   r   r   r   Útest_jacobi_precise  s,    ý
ý
ý
ýrC   c                  C   s(  t ddƒ\} }dd„ | D ƒddgks(t‚dd„ |D ƒddgksBt‚t d	dƒ\} }d
d„ | D ƒdddgkslt‚dd„ |D ƒdddgksˆt‚t ddƒ\} }dd„ | D ƒddddgks´t‚dd„ |D ƒddddgksÒt‚t ddƒ\} }dd„ | D ƒdddddgkst‚dd„ |D ƒdddddgks$t‚d S )Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   $  s     z test_lobatto.<locals>.<listcomp>ú-1Ú1c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   '  s     r   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ,  s     r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   0  s     z0.33333333333333333z1.3333333333333333r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   6  s     z-0.44721359549995794z0.44721359549995794c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ;  s     z0.16666666666666667z0.83333333333333333r$   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   B  s     z-0.65465367070797714z0.65465367070797714c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   H  s     z0.10000000000000000z0.54444444444444444z0.71111111111111111©r   r   r   r   r   r   Útest_lobatto"  s`    þ
þ
ý
ý
ü
ü
ûûrG   c                  C   sJ   t ddƒ\} }dd„ | D ƒdddgks*t‚dd„ |D ƒd	d
d	gksFt‚d S )Nr   r"   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   R  s     z(test_lobatto_precise.<locals>.<listcomp>rD   r   rE   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   V  s     z*0.3333333333333333333333333333333333333333z)1.333333333333333333333333333333333333333rF   r   r   r   r   Útest_lobatto_preciseP  s    ý
ýrH   N)Z
sympy.corer   r   Zsympy.integrals.quadraturer   r   r   r   r   r	   r
   r   r!   r#   r&   r'   r,   r-   r1   r2   r:   r;   r?   r@   rB   rC   rG   rH   r   r   r   r   Ú<module>   s"   ($42b22b.