a
    kº”hÏM  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 )$é    )ÚSÚRational)Úgauss_legendreÚgauss_laguerreÚgauss_hermiteÚgauss_gen_laguerreÚgauss_chebyshev_tÚgauss_chebyshev_uÚgauss_jacobiÚgauss_lobattoc                  C   s
  t ddƒ\} }dd„ | D ƒdgks&J ‚dd„ |D ƒdgks>J ‚t ddƒ\} }d	d„ | D ƒd
dgksfJ ‚dd„ |D ƒddgks€J ‚t ddƒ\} }dd„ | D ƒg d¢ks¨J ‚dd„ |D ƒg d¢ksÂJ ‚t ddƒ\} }dd„ | D ƒg d¢ksêJ ‚dd„ |D ƒg d¢ksJ ‚d S )Né   é   c                 S   s   g | ]}t |ƒ‘qS © ©Ústr©Ú.0Úrr   r   úS/var/www/auris/lib/python3.9/site-packages/sympy/integrals/tests/test_quadrature.pyÚ
<listcomp>
   ó    z!test_legendre.<locals>.<listcomp>Ú0c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   ú2.0000000000000000é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   z-0.57735026918962576z0.57735026918962576c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   ú1.0000000000000000é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   )z-0.77459666924148338r   z0.77459666924148338c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   )ú0.55555555555555556z0.88888888888888889r   é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r       r   )z-0.86113631159405258z-0.33998104358485626z0.33998104358485626z0.86113631159405258c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   %   r   )ú0.34785484513745386ú0.65214515486254614r   r   ©r   ©ÚxÚwr   r   r   Útest_legendre   s$    þ
þ
r$   c                  C   sF   t ddƒ\} }dd„ | D ƒg d¢ks(J ‚dd„ |D ƒg d¢ksBJ ‚d S )Nr   é(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   .   r   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   r   )ú*0.5555555555555555555555555555555555555556z*0.8888888888888888888888888888888888888889r&   r    r!   r   r   r   Útest_legendre_precise,   s    r'   c                  C   sP  t ddƒ\} }dd„ | D ƒdgks&J ‚dd„ |D ƒdgks>J ‚t ddƒ\} }dd„ | D ƒd	d
gksfJ ‚dd„ |D ƒddgks€J ‚t ddƒ\} }dd„ | D ƒg d¢ks¨J ‚dd„ |D ƒg d¢ksÂJ ‚t ddƒ\} }dd„ | D ƒg d¢ksêJ ‚dd„ |D ƒg d¢ksJ ‚t ddƒ\} }dd„ | D ƒg d¢ks0J ‚dd„ |D ƒg d¢ksLJ ‚d S )Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   :   r   z!test_laguerre.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ;   r   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   >   r   z0.58578643762690495z3.4142135623730950c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   A   r   z0.85355339059327376z0.14644660940672624r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   F   r   )z0.41577455678347908z2.2942803602790417z6.2899450829374792c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   K   r   )z0.71109300992917302z0.27851773356924085z0.010389256501586136r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   R   r   )z0.32254768961939231z1.7457611011583466z4.5366202969211280z9.3950709123011331c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   W   r   )z0.60315410434163360z0.35741869243779969z0.038887908515005384z0.00053929470556132745é   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ^   r   )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   r   )z0.52175561058280865z0.39866681108317593z0.075942449681707595z0.0036117586799220485z2.3369972385776228e-5©r   r!   r   r   r   Útest_laguerre8   s*    þ
þ
r*   c                  C   sF   t ddƒ\} }dd„ | D ƒg d¢ks(J ‚dd„ |D ƒg d¢ksBJ ‚d S )Nr   r%   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   n   r   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   r   )z*0.7110930099291730154495901911425944313094z*0.2785177335692408488014448884567264810349z+0.01038925650158613574896492040067908765572r)   r!   r   r   r   Útest_laguerre_precisel   s    r+   c                  C   sP  t ddƒ\} }dd„ | D ƒdgks&J ‚dd„ |D ƒdgks>J ‚t ddƒ\} }d	d„ | D ƒd
dgksfJ ‚dd„ |D ƒddgks€J ‚t ddƒ\} }dd„ | D ƒg d¢ks¨J ‚dd„ |D ƒg d¢ksÂJ ‚t ddƒ\} }dd„ | D ƒg d¢ksêJ ‚dd„ |D ƒg d¢ksJ ‚t ddƒ\} }dd„ | D ƒg d¢ks0J ‚dd„ |D ƒg d¢ksLJ ‚d S )Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   z   r   z test_hermite.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   {   r   ú1.7724538509055160r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ~   r   ú-0.70710678118654752ú0.70710678118654752c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   z0.88622692545275801r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   †   r   )z-1.2247448713915890r   z1.2247448713915890c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Š   r   )ú0.29540897515091934z1.1816359006036774r/   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   )z-1.6506801238857846z-0.52464762327529032z0.52464762327529032z1.6506801238857846c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   •   r   )ú0.081312835447245177ú0.80491409000551284r1   r0   r(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   œ   r   )z-2.0201828704560856z-0.95857246461381851r   z0.95857246461381851z2.0201828704560856c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¢   r   )ú0.019953242059045913ú0.39361932315224116z0.94530872048294188r3   r2   ©r   r!   r   r   r   Útest_hermitex   s*    þ
þ
r5   c                  C   sF   t ddƒ\} }dd„ | D ƒg d¢ks(J ‚dd„ |D ƒg d¢ksBJ ‚d S )Nr   r%   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¬   r   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   °   r   )ú*0.2954089751509193378830279138901908637996z)1.181635900603677351532111655560763455198r6   r4   r!   r   r   r   Útest_hermite_preciseª   s    r7   c                  C   sÞ  t dtddƒdƒ\} }dd„ | D ƒdgks.J ‚dd„ |D ƒd	gksFJ ‚t dtddƒdƒ\} }d
d„ | D ƒddgksvJ ‚dd„ |D ƒddgksJ ‚t dtddƒdƒ\} }dd„ | D ƒg d¢ksÀJ ‚dd„ |D ƒg d¢ksÚJ ‚t dtddƒdƒ\} }dd„ | D ƒg d¢ksJ ‚dd„ |D ƒg d¢ks(J ‚t dtddƒdƒ\} }dd„ | D ƒg d¢ksZJ ‚dd„ |D ƒg d¢ksvJ ‚t dddƒ\} }dd„ | D ƒd gks J ‚d!d„ |D ƒd"gksºJ ‚t dddƒ\} }d#d„ | D ƒd"d$gksæJ ‚d%d„ |D ƒd&dgksJ ‚t dddƒ\} }d'd„ | D ƒg d(¢ks.J ‚d)d„ |D ƒg d*¢ksJJ ‚t dddƒ\} }d+d„ | D ƒg d,¢ksvJ ‚d-d„ |D ƒg d.¢ks’J ‚t dddƒ\} }d/d„ | D ƒg d0¢ks¾J ‚d1d„ |D ƒg d2¢ksÚJ ‚d S )3Nr   éÿÿÿÿr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¸   r   z%test_gen_laguerre.<locals>.<listcomp>ú0.50000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¹   r   r,   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¼   r   z0.27525512860841095z2.7247448713915890c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¿   r   z1.6098281800110257z0.16262567089449035r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ä   r   )z0.19016350919348813z1.7844927485432516z5.5253437422632603c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   È   r   )z1.4492591904487850z0.31413464064571329z0.0090600198110176913r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Î   r   )z0.14530352150331709z1.3390972881263614z3.9269635013582872z8.5886356890120343c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ó   r   )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   r   )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   r   )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   r   z3.0000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   é   r   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ì   r   z6.0000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ï   r   z1.5000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ô   r   )z1.5173870806774125z4.3115831337195203z9.1710297856030672c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ø   r   )z1.0374949614904253z0.90575000470306537z0.056755033806509347c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   þ   r   )z1.2267632635003021z3.4125073586969460z6.9026926058516134z12.458036771951139c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     r   )z0.72552499769865438z1.0634242919791946z0.20669613102835355z0.0043545792937974889c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   
  r   )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     r   )z0.52091739683509184z1.0667059331592211z0.38354972366693113z0.028564233532974658z0.00026271280578124935©r   r   r!   r   r   r   Útest_gen_laguerre¶   sT    þ
þ
þþr;   c                  C   s’   t dtddƒdƒ\} }dd„ | D ƒg d¢ks0J ‚dd„ |D ƒg d	¢ksJJ ‚t dddƒ\} }d
d„ | D ƒg d¢kstJ ‚dd„ |D ƒg d¢ksŽJ ‚d S )Nr   r8   r   r%   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     r   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     r   )z)1.449259190448785048183829411195134343108z*0.3141346406457132878326231270167565378246z,0.009060019811017691281714945129254301865020c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   $  r   )z)1.517387080677412495020323111016672547482z)4.311583133719520302881184669723530562299z)9.171029785603067202098492219259796890218c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   (  r   )z)1.037494961490425285817554606541269153041z*0.9057500047030653669269785048806009945254z+0.05675503380650934725546688857812985243312r:   r!   r   r   r   Útest_gen_laguerre_precise  s    r<   c                  C   sP  t ddƒ\} }dd„ | D ƒdgks&J ‚dd„ |D ƒdgks>J ‚t ddƒ\} }d	d„ | D ƒd
dgksfJ ‚dd„ |D ƒddgks€J ‚t ddƒ\} }dd„ | D ƒg d¢ks¨J ‚dd„ |D ƒg d¢ksÂJ ‚t ddƒ\} }dd„ | D ƒg d¢ksêJ ‚dd„ |D ƒg d¢ksJ ‚t ddƒ\} }dd„ | D ƒg d¢ks0J ‚dd„ |D ƒg d¢ksLJ ‚d S )Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   0  r   z$test_chebyshev_t.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   1  r   ú3.1415926535897932r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   4  r   r.   r-   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   7  r   ú1.5707963267948966r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   <  r   )ú0.86602540378443865r   ú-0.86602540378443865c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   @  r   )ú1.0471975511965977rA   rA   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   F  r   )z0.92387953251128676z0.38268343236508977z-0.38268343236508977z-0.92387953251128676c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   K  r   )ú0.78539816339744831rB   rB   rB   r(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   R  r   )z0.95105651629515357z0.58778525229247313r   z-0.58778525229247313z-0.95105651629515357c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   X  r   )ú0.62831853071795865rC   rC   rC   rC   ©r   r!   r   r   r   Útest_chebyshev_t.  s*    þ
þ
rE   c                  C   sF   t ddƒ\} }dd„ | D ƒg d¢ks(J ‚dd„ |D ƒg d¢ksBJ ‚d S )Nr   r%   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   b  r   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  r   )ú)1.047197551196597746154214461093167628066rF   rF   rD   r!   r   r   r   Útest_chebyshev_t_precise`  s    rG   c                  C   sP  t ddƒ\} }dd„ | D ƒdgks&J ‚dd„ |D ƒdgks>J ‚t ddƒ\} }d	d„ | D ƒd
dgksfJ ‚dd„ |D ƒddgks€J ‚t ddƒ\} }dd„ | D ƒg d¢ks¨J ‚dd„ |D ƒg d¢ksÂJ ‚t ddƒ\} }dd„ | D ƒg d¢ksêJ ‚dd„ |D ƒg d¢ksJ ‚t ddƒ\} }dd„ | D ƒg d¢ks0J ‚dd„ |D ƒg d¢ksLJ ‚d S )Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   n  r   z$test_chebyshev_u.<locals>.<listcomp>r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   o  r   r>   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   r  r   r9   ú-0.50000000000000000c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   u  r   rB   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   z  r   )r.   r   r-   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ~  r   )ú0.39269908169872415rB   rI   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   „  r   )ú0.80901699437494742z0.30901699437494742ú-0.30901699437494742z-0.80901699437494742c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ‰  r   )ú0.21707871342270599ú0.56831944997474231rM   rL   r(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     r   )r?   r9   r   rH   r@   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   –  r   )ú0.13089969389957472rI   z0.52359877559829887rI   rN   ©r	   r!   r   r   r   Útest_chebyshev_ul  s*    þ
þ
rP   c                  C   sF   t ddƒ\} }dd„ | D ƒg d¢ks(J ‚dd„ |D ƒg d¢ksBJ ‚d S )Nr   r%   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r      r   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   ¤  r   )ú*0.3926990816987241548078304229099378605246z*0.7853981633974483096156608458198757210493rQ   rO   r!   r   r   r   Útest_chebyshev_u_precisež  s    rR   c                  C   sü  t dtddƒtjdƒ\} }dd„ | D ƒdgks2J ‚dd„ |D ƒd	gksJJ ‚t dtddƒtjdƒ\} }d
d„ | D ƒddgks~J ‚dd„ |D ƒddgks˜J ‚t dtddƒtjdƒ\} }dd„ | D ƒg d¢ksÌJ ‚dd„ |D ƒg d¢ksæJ ‚t dtddƒtjdƒ\} }dd„ | D ƒg d¢ksJ ‚dd„ |D ƒg d¢ks8J ‚t dtddƒtjdƒ\} }dd„ | D ƒg d¢ksnJ ‚dd„ |D ƒg d¢ksŠJ ‚t ddddƒ\} }dd„ | D ƒd gks¶J ‚d!d„ |D ƒd"gksÐJ ‚t ddddƒ\} }d#d„ | D ƒd$d%gksþJ ‚d&d„ |D ƒd'd(gksJ ‚t ddddƒ\} }d)d„ | D ƒg d*¢ksHJ ‚d+d„ |D ƒg d,¢ksdJ ‚t ddddƒ\} }d-d„ | D ƒg d.¢ks’J ‚d/d„ |D ƒg d0¢ks®J ‚t ddddƒ\} }d1d„ | D ƒg d2¢ksÜJ ‚d3d„ |D ƒg d4¢ksøJ ‚d S )5Nr   r8   r   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¬  r   ztest_jacobi.<locals>.<listcomp>r9   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ­  r   r=   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   °  r   rK   rJ   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ³  r   z0.86831485369082398z2.2732777998989693r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¸  r   )z-0.62348980185873353z0.22252093395631440z0.90096886790241913c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ¼  r   )z0.33795476356635433z1.0973322242791115z1.7063056657443274r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Â  r   )z-0.76604444311897804z-0.17364817766693035r9   z0.93969262078590838c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ç  r   )z0.16333179083642836z0.57690240318269103rA   z1.3541609083740761r(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Î  r   )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  r   )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  r   z0.14285714285714286c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   Ý  r   z1.0666666666666667c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   à  r   z-0.24025307335204215z0.46247529557426437c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ã  r   z0.48514624517838660z0.58152042148828007c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   è  r   )z-0.46115870378089762z0.10438533038323902z0.62950064612493132c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ì  r   )z0.17937613502213266z0.61595640991147154z0.27133412173306246c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ò  r   )z-0.59903470850824782z-0.14761105199952565z0.32554377081188859z0.72879429738819258c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ÷  r   )z0.067809641836772187z0.38956404952032481z0.47995970868024150z0.12933326662932816c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   þ  r   )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     r   )z0.027410178066337099z0.21291786060364828z0.43908437944395081z0.32220656547221822z0.065047683080512268©r
   r   r   ZHalfr!   r   r   r   Útest_jacobiª  sT    þ
þ
þþrT   c                  C   s˜   t dtddƒtjdƒ\} }dd„ | D ƒg d¢ks4J ‚dd„ |D ƒg d	¢ksNJ ‚t ddddƒ\} }d
d„ | D ƒg d¢kszJ ‚dd„ |D ƒg d¢ks”J ‚d S )Nr   r8   r   r%   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     r   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     r   )z*0.3379547635663543330553835737094171534907z)1.097332224279111467485302294320899710461z)1.706305665744327437921957515249186020246c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     r   )z+-0.4611587037808976179121958105554375981274z*0.1043853303832390210914918407615869143233z*0.6295006461249313240934312425211234110769c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r     r   )z*0.1793761350221326596137764371503859752628z*0.6159564099114715430909548532229749439714z*0.2713341217330624639619353762933057474325rS   r!   r   r   r   Útest_jacobi_precise  s    rU   c                  C   s  t ddƒ\} }dd„ | D ƒddgks(J ‚dd„ |D ƒddgksBJ ‚t d	dƒ\} }d
d„ | D ƒg d¢ksjJ ‚dd„ |D ƒg d¢ks„J ‚t ddƒ\} }dd„ | D ƒg d¢ks¬J ‚dd„ |D ƒg d¢ksÆJ ‚t ddƒ\} }dd„ | D ƒg d¢ksîJ ‚dd„ |D ƒg d¢ks
J ‚d S )Nr   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   $  r   z test_lobatto.<locals>.<listcomp>ú-1Ú1c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   '  r   r   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ,  r   ©rV   r   rW   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   0  r   )ú0.33333333333333333z1.3333333333333333rY   r   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   6  r   )rV   z-0.44721359549995794z0.44721359549995794rW   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   ;  r   )ú0.16666666666666667ú0.83333333333333333r[   rZ   r(   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   B  r   )rV   z-0.65465367070797714r   z0.65465367070797714rW   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   H  r   )ú0.10000000000000000ú0.54444444444444444z0.71111111111111111r]   r\   ©r   r!   r   r   r   Útest_lobatto"  s$    þ
þ
r_   c                  C   sF   t ddƒ\} }dd„ | D ƒg d¢ks(J ‚dd„ |D ƒg d¢ksBJ ‚d S )Nr   r%   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   R  r   z(test_lobatto_precise.<locals>.<listcomp>rX   c                 S   s   g | ]}t |ƒ‘qS r   r   r   r   r   r   r   V  r   )ú*0.3333333333333333333333333333333333333333z)1.333333333333333333333333333333333333333r`   r^   r!   r   r   r   Útest_lobatto_preciseP  s    ra   N)Z
sympy.corer   r   Zsympy.integrals.quadraturer   r   r   r   r   r	   r
   r   r$   r'   r*   r+   r5   r7   r;   r<   rE   rG   rP   rR   rT   rU   r_   ra   r   r   r   r   Ú<module>   s"   ($42b22b.