
    gM                         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 Zd Zd Zd Zd Zd Zd	 Zd
 Zd Zd Zd Zd Zd Zd Zd Zd ZdS )    )SRational)gauss_legendregauss_laguerregauss_hermitegauss_gen_laguerregauss_chebyshev_tgauss_chebyshev_ugauss_jacobigauss_lobattoc                     t          dd          \  } }d | D             dgk    sJ d |D             dgk    sJ t          dd          \  } }d | D             d	d
gk    sJ d |D             ddgk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )N      c                 ,    g | ]}t          |          S  str.0rs     a/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/integrals/tests/test_quadrature.py
<listcomp>z!test_legendre.<locals>.<listcomp>
       qCFF    0c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_legendre.<locals>.<listcomp>   r   r   2.0000000000000000   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_legendre.<locals>.<listcomp>   r   r   z-0.57735026918962576z0.57735026918962576c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_legendre.<locals>.<listcomp>   r   r   1.0000000000000000   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_legendre.<locals>.<listcomp>   r   r   )z-0.77459666924148338r   z0.77459666924148338c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_legendre.<locals>.<listcomp>   r   r   )0.55555555555555556z0.88888888888888889r%      c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_legendre.<locals>.<listcomp>    r   r   )z-0.86113631159405258z-0.33998104358485626z0.33998104358485626z0.86113631159405258c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_legendre.<locals>.<listcomp>%   r   r   )0.347854845137453860.65214515486254614r*   r)   r   xws     r   test_legendrer/      s   !R  DAqA3%''''A#7"88888!R  DAqA"!## # # # # A  #" " " " " !R  DAqA ## ## ## # # # # A ## ## ## # # # #
 !R  DAqA ## ## ## # # # #
 A ## ## ## # # # # # #r   c                  |    t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr"   (   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z)test_legendre_precise.<locals>.<listcomp>.   r   r   )z+-0.7745966692414833770358530799564799221666r   z*0.7745966692414833770358530799564799221666c                 ,    g | ]}t          |          S r   r   r   s     r   r   z)test_legendre_precise.<locals>.<listcomp>2   r   r   )*0.5555555555555555555555555555555555555556z*0.8888888888888888888888888888888888888889r4   r+   r,   s     r   test_legendre_preciser5   ,   s    !R  DAqA #: #: #: : : : : A #: #: #: : : : : : :r   c                  P   t          dd          \  } }d | D             dgk    sJ d |D             dgk    sJ t          dd          \  } }d | D             dd	gk    sJ d
 |D             ddgk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>:   r   r   r!   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>;   r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>>   r   r   z0.58578643762690495z3.4142135623730950c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>A   r   r   z0.85355339059327376z0.14644660940672624r"   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>F   r   r   )z0.41577455678347908z2.2942803602790417z6.2899450829374792c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>K   r   r   )z0.71109300992917302z0.27851773356924085z0.010389256501586136r&   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>R   r   r   )z0.32254768961939231z1.7457611011583466z4.5366202969211280z9.3950709123011331c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>W   r   r   )z0.60315410434163360z0.35741869243779969z0.038887908515005384z0.00053929470556132745   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>^   r   r   )z0.26356031971814091z1.4134030591065168z3.5964257710407221z7.0858100058588376z12.640800844275783c                 ,    g | ]}t          |          S r   r   r   s     r   r   z!test_laguerre.<locals>.<listcomp>d   r   r   )z0.52175561058280865z0.39866681108317593z0.075942449681707595z0.0036117586799220485z2.3369972385776228e-5r   r,   s     r   test_laguerrerC   8   sW   !R  DAqA#7"88888A#7"88888!R  DAqA! #" " " " " A!!## # # # # !R  DAqA # # #    
 A # # #     !R  DAqA #" #" #" " " " "
 A #& #& #& & & & & !R  DAqA #" #" #" " " " " A #% #% #% % % % % % %r   c                  |    t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr"   r1   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z)test_laguerre_precise.<locals>.<listcomp>n   r   r   )z*0.4157745567834790833115338731282744735466z)2.294280360279041719822050361359593868960z)6.289945082937479196866415765512131657493c                 ,    g | ]}t          |          S r   r   r   s     r   r   z)test_laguerre_precise.<locals>.<listcomp>r   r   r   )z*0.7110930099291730154495901911425944313094z*0.2785177335692408488014448884567264810349z+0.01038925650158613574896492040067908765572rB   r,   s     r   test_laguerre_preciserG   l   s    !R  DAqA #9 #9 #9 9 9 9 9 A #; #; #; ; ; ; ; ; ;r   c                  P   t          dd          \  } }d | D             dgk    sJ d |D             dgk    sJ t          dd          \  } }d | D             d	d
gk    sJ d |D             ddgk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>z   r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>{   r   r   1.7724538509055160r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>~   r   r   -0.707106781186547520.70710678118654752c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>   r   r   z0.88622692545275801r"   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>   r   r   )z-1.2247448713915890r   z1.2247448713915890c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>   r   r   )0.29540897515091934z1.1816359006036774rR   r&   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>   r   r   )z-1.6506801238857846z-0.52464762327529032z0.52464762327529032z1.6506801238857846c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>   r   r   )0.0813128354472451770.80491409000551284rV   rU   r?   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>   r   r   )z-2.0201828704560856z-0.95857246461381851r   z0.95857246461381851z2.0201828704560856c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_hermite.<locals>.<listcomp>   r   r   )0.0199532420590459130.39361932315224116z0.94530872048294188rZ   rY   r   r,   s     r   test_hermiter\   x   sU   BDAqA3%''''A#7"88888BDAqA"!## # # # # A!!## # # # # BDAqA #" #" #" " " " " A ## ## ## # # # #
 BDAqA #" #" #" " " " "
 A #$ #$ #$ $ $ $ $ BDAqA #" #" #" " " " " A #$ #$ #$ $ $ $ $ $ $r   c                  |    t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr"   r1   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z(test_hermite_precise.<locals>.<listcomp>   r   r   )z*-1.224744871391589049098642037352945695983r   z)1.224744871391589049098642037352945695983c                 ,    g | ]}t          |          S r   r   r   s     r   r   z(test_hermite_precise.<locals>.<listcomp>   r   r   )*0.2954089751509193378830279138901908637996z)1.181635900603677351532111655560763455198r`   r[   r,   s     r   test_hermite_precisera      s    BDAqA #5 #5 #5 5 5 5 5 A #6 #6 #6 6 6 6 6 6 6r   c                  :   t          dt          dd          d          \  } }d | D             dgk    sJ d |D             dgk    sJ t          dt          dd          d          \  } }d	 | D             d
dgk    sJ d |D             ddgk    sJ t          dt          dd          d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dt          dd          d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dt          dd          d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          ddd          \  } }d | D             dgk    sJ d  |D             d!gk    sJ t          ddd          \  } }d" | D             d!d#gk    sJ d$ |D             d%dgk    sJ t          ddd          \  } }d& | D             g d'k    sJ d( |D             g d)k    sJ t          ddd          \  } }d* | D             g d+k    sJ d, |D             g d-k    sJ t          ddd          \  } }d. | D             g d/k    sJ d0 |D             g d1k    sJ d S )2Nr   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   0.50000000000000000c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   rK   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   z0.27525512860841095z2.7247448713915890c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   z1.6098281800110257z0.16262567089449035r"   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z0.19016350919348813z1.7844927485432516z5.5253437422632603c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z1.4492591904487850z0.31413464064571329z0.0090600198110176913r&   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z0.14530352150331709z1.3390972881263614z3.9269635013582872z8.5886356890120343c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z1.3222940251164826z0.41560465162978376z0.034155966014826951z0.00039920814442273524r?   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z0.11758132021177814z1.0745620124369040z3.0859374437175500z6.4147297336620305z11.807189489971737c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z1.2217252674706516z0.48027722216462937z0.067748788910962126z0.0026872914935624654z1.5280865710465241e-5c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   z3.0000000000000000c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   z6.0000000000000000c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   z1.5000000000000000c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z1.5173870806774125z4.3115831337195203z9.1710297856030672c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z1.0374949614904253z0.90575000470306537z0.056755033806509347c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>   r   r   )z1.2267632635003021z3.4125073586969460z6.9026926058516134z12.458036771951139c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>  r   r   )z0.72552499769865438z1.0634242919791946z0.20669613102835355z0.0043545792937974889c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>
  r   r   )z1.0311091440933816z2.8372128239538217z5.6202942725987079z9.6829098376640271z15.828473921690062c                 ,    g | ]}t          |          S r   r   r   s     r   r   z%test_gen_laguerre.<locals>.<listcomp>  r   r   )z0.52091739683509184z1.0667059331592211z0.38354972366693113z0.028564233532974658z0.00026271280578124935r   r   r,   s     r   test_gen_laguerrerz      s   a"a"55DAqA#8"99999A#7"88888a"a"55DAqA! #" " " " " A !## # # # # a"a"55DAqA #" #" #" " " " " A #% #% #% % % % %
 a"a"55DAqA #" #" #" " " " "
 A #& #& #& & & & & a"a"55DAqA #" #" #" " " " " A #% #% #% % % % % aB''DAqA#7"88888A#7"88888aB''DAqA  #" " " " " A !## # # # # aB''DAqA #" #" #" " " " " A #$ #$ #$ $ $ $ $
 aB''DAqA #" #" #" " " " "
 A #% #% #% % % % % aB''DAqA #" #" #" " " " " A #& #& #& & & & & & &r   c                     t          dt          dd          d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          ddd          \  } }d	 | D             g d
k    sJ d |D             g dk    sJ d S )Nr"   rc   r   r1   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z-test_gen_laguerre_precise.<locals>.<listcomp>  r   r   )z*0.1901635091934881328718554276203028970878z)1.784492748543251591186722461957367638500z)5.525343742263260275941422110422329464413c                 ,    g | ]}t          |          S r   r   r   s     r   r   z-test_gen_laguerre_precise.<locals>.<listcomp>  r   r   )z)1.449259190448785048183829411195134343108z*0.3141346406457132878326231270167565378246z,0.009060019811017691281714945129254301865020c                 ,    g | ]}t          |          S r   r   r   s     r   r   z-test_gen_laguerre_precise.<locals>.<listcomp>$  r   r   )z)1.517387080677412495020323111016672547482z)4.311583133719520302881184669723530562299z)9.171029785603067202098492219259796890218c                 ,    g | ]}t          |          S r   r   r   s     r   r   z-test_gen_laguerre_precise.<locals>.<listcomp>(  r   r   )z)1.037494961490425285817554606541269153041z*0.9057500047030653669269785048806009945254z+0.05675503380650934725546688857812985243312ry   r,   s     r   test_gen_laguerre_preciser     s   a"a"55DAqA #9 #9 #9 9 9 9 9 A #< #< #< < < < <
 aB''DAqA #9 #9 #9 9 9 9 9 A #; #; #; ; ; ; ; ; ;r   c                  P   t          dd          \  } }d | D             dgk    sJ d |D             dgk    sJ t          dd          \  } }d | D             d	d
gk    sJ d |D             ddgk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>0  r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>1  r   r   3.1415926535897932r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>4  r   r   rN   rM   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>7  r   r   1.5707963267948966r"   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp><  r   r   )0.86602540378443865r   -0.86602540378443865c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>@  r   r   )1.0471975511965977r   r   r&   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>F  r   r   )z0.92387953251128676z0.38268343236508977z-0.38268343236508977z-0.92387953251128676c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>K  r   r   )0.78539816339744831r   r   r   r?   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>R  r   r   )z0.95105651629515357z0.58778525229247313r   z-0.58778525229247313z-0.95105651629515357c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_t.<locals>.<listcomp>X  r   r   )0.62831853071795865r   r   r   r   r	   r,   s     r   test_chebyshev_tr   .  sU   Q##DAqA3%''''A#7"88888Q##DAqA!"#$ $ $ $ $ A  #" " " " " Q##DAqA #$ #$ #$ $ $ $ $ A #" #" #" " " " "
 Q##DAqA #$ #$ #$ $ $ $ $
 A ## ## ## # # # # Q##DAqA #$ #$ #$ $ $ $ $ A ## ## ## # # # # # #r   c                  |    t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr"   r1   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z,test_chebyshev_t_precise.<locals>.<listcomp>b  r   r   )z*0.8660254037844386467637231707529361834714r   z+-0.8660254037844386467637231707529361834714c                 ,    g | ]}t          |          S r   r   r   s     r   r   z,test_chebyshev_t_precise.<locals>.<listcomp>f  r   r   ))1.047197551196597746154214461093167628066r   r   r   r,   s     r   test_chebyshev_t_preciser   `  s    Q##DAqA #; #; #; ; ; ; ; A #9 #9 #9 9 9 9 9 9 9r   c                  P   t          dd          \  } }d | D             dgk    sJ d |D             dgk    sJ t          dd          \  } }d | D             d	d
gk    sJ d |D             ddgk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>n  r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>o  r   r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>r  r   r   re   -0.50000000000000000c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>u  r   r   r   r"   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>z  r   r   )rN   r   rM   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>~  r   r   )0.39269908169872415r   r   r&   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>  r   r   )0.80901699437494742z0.30901699437494742-0.30901699437494742z-0.80901699437494742c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>  r   r   )0.217078713422705990.56831944997474231r   r   r?   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>  r   r   )r   re   r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z$test_chebyshev_u.<locals>.<listcomp>  r   r   )0.13089969389957472r   z0.52359877559829887r   r   r
   r,   s     r   test_chebyshev_ur   l  sU   Q##DAqA3%''''A#7"88888Q##DAqA!"#$ $ $ $ $ A!!## # # # # Q##DAqA #$ #$ #$ $ $ $ $ A ## ## ## # # # #
 Q##DAqA #$ #$ #$ $ $ $ $
 A ## ## ## # # # # Q##DAqA #$ #$ #$ $ $ $ $ A ## ## ## # # # # # #r   c                  |    t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr"   r1   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z,test_chebyshev_u_precise.<locals>.<listcomp>  r   r   )z*0.7071067811865475244008443621048490392848r   z+-0.7071067811865475244008443621048490392848c                 ,    g | ]}t          |          S r   r   r   s     r   r   z,test_chebyshev_u_precise.<locals>.<listcomp>  r   r   )*0.3926990816987241548078304229099378605246z*0.7853981633974483096156608458198757210493r   r   r,   s     r   test_chebyshev_u_preciser     s    Q##DAqA #; #; #; ; ; ; ; A #: #: #: : : : : : :r   c                     t          dt          dd          t          j        d          \  } }d | D             dgk    sJ d |D             dgk    sJ t          dt          dd          t          j        d          \  } }d	 | D             d
dgk    sJ d |D             ddgk    sJ t          dt          dd          t          j        d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dt          dd          t          j        d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dt          dd          t          j        d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dddd          \  } }d | D             dgk    sJ d  |D             d!gk    sJ t          dddd          \  } }d" | D             d#d$gk    sJ d% |D             d&d'gk    sJ t          dddd          \  } }d( | D             g d)k    sJ d* |D             g d+k    sJ t          dddd          \  } }d, | D             g d-k    sJ d. |D             g d/k    sJ t          dddd          \  } }d0 | D             g d1k    sJ d2 |D             g d3k    sJ d S )4Nr   rc   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   re   c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   z0.86831485369082398z2.2732777998989693r"   c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z-0.62348980185873353z0.22252093395631440z0.90096886790241913c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z0.33795476356635433z1.0973322242791115z1.7063056657443274r&   c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z-0.76604444311897804z-0.17364817766693035re   z0.93969262078590838c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z0.16333179083642836z0.57690240318269103r   z1.3541609083740761r?   c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z-0.84125353283118117z-0.41541501300188643z0.14231483827328514z0.65486073394528506z0.95949297361449739c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z0.090675770007435372z0.33391416373675607z0.65248870981926643z0.94525424081394926z1.1192597692123861c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   z0.14285714285714286c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   z1.0666666666666667c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   z-0.24025307335204215z0.46247529557426437c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   z0.48514624517838660z0.58152042148828007c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z-0.46115870378089762z0.10438533038323902z0.62950064612493132c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z0.17937613502213266z0.61595640991147154z0.27133412173306246c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z-0.59903470850824782z-0.14761105199952565z0.32554377081188859z0.72879429738819258c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z0.067809641836772187z0.38956404952032481z0.47995970868024150z0.12933326662932816c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z-0.69045775012676106z-0.32651993134900065z0.082337849552034905z0.47517887061283164z0.79279429464422850c                 ,    g | ]}t          |          S r   r   r   s     r   r   ztest_jacobi.<locals>.<listcomp>  r   r   )z0.027410178066337099z0.21291786060364828z0.43908437944395081z0.32220656547221822z0.065047683080512268r   r   r   Halfr,   s     r   test_jacobir     s   8B??AFB77DAqA#8"99999A#7"888888B??AFB77DAqA"!## # # # # A! #" " " " " 8B??AFB77DAqA ## ## ## # # # # A #" #" #" " " " "
 8B??AFB77DAqA ## ## ## # # # #
 A #" #" #" " " " " 8B??AFB77DAqA ## ## ## # # # # A #" #" #" " " " " 1a$$DAqA#8"99999A#7"888881a$$DAqA"!## # # # # A!!## # # # # 1a$$DAqA ## ## ## # # # # A ## ## ## # # # #
 1a$$DAqA ## ## ## # # # #
 A ## ## ## # # # # 1a$$DAqA ## ## ## # # # # A #$ #$ #$ $ $ $ $ $ $r   c                  *   t          dt          dd          t          j        d          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dddd          \  } }d	 | D             g d
k    sJ d |D             g dk    sJ d S )Nr"   rc   r   r1   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z'test_jacobi_precise.<locals>.<listcomp>  r   r   )z+-0.6234898018587335305250048840042398106323z*0.2225209339563144042889025644967947594664z*0.9009688679024191262361023195074450511659c                 ,    g | ]}t          |          S r   r   r   s     r   r   z'test_jacobi_precise.<locals>.<listcomp>  r   r   )z*0.3379547635663543330553835737094171534907z)1.097332224279111467485302294320899710461z)1.706305665744327437921957515249186020246c                 ,    g | ]}t          |          S r   r   r   s     r   r   z'test_jacobi_precise.<locals>.<listcomp>  r   r   )z+-0.4611587037808976179121958105554375981274z*0.1043853303832390210914918407615869143233z*0.6295006461249313240934312425211234110769c                 ,    g | ]}t          |          S r   r   r   s     r   r   z'test_jacobi_precise.<locals>.<listcomp>  r   r   )z*0.1793761350221326596137764371503859752628z*0.6159564099114715430909548532229749439714z*0.2713341217330624639619353762933057474325r   r,   s     r   test_jacobi_preciser     s   8B??AFB77DAqA #: #: #: : : : : A #9 #9 #9 9 9 9 9
 1a$$DAqA #: #: #: : : : : A #: #: #: : : : : : :r   c                     t          dd          \  } }d | D             ddgk    sJ d |D             ddgk    sJ t          dd          \  } }d	 | D             g d
k    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>$  r   r   -11c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>'  r   r   r!   r"   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>,  r   r   r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>0  r   r   )0.33333333333333333z1.3333333333333333r   r&   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>6  r   r   )r   z-0.44721359549995794z0.44721359549995794r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>;  r   r   )0.166666666666666670.83333333333333333r   r   r?   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>B  r   r   )r   z-0.65465367070797714r   z0.65465367070797714r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z test_lobatto.<locals>.<listcomp>H  r   r   )0.100000000000000000.54444444444444444z0.71111111111111111r   r   r   r,   s     r   test_lobattor   "  s   BDAqA#     A  #" " " " " BDAqA # # #     A ## ## ## # # # #
 BDAqA # # #    
 A ## ## ## # # # # BDAqA # # #     A ## ## ## # # # # # #r   c                  |    t          dd          \  } }d | D             g dk    sJ d |D             g dk    sJ d S )Nr"   r1   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z(test_lobatto_precise.<locals>.<listcomp>R  r   r   r   c                 ,    g | ]}t          |          S r   r   r   s     r   r   z(test_lobatto_precise.<locals>.<listcomp>V  r   r   )*0.3333333333333333333333333333333333333333z)1.333333333333333333333333333333333333333r   r   r,   s     r   test_lobatto_preciser   P  s    BDAqA # # #     A #: #: #: : : : : : :r   N)
sympy.corer   r   sympy.integrals.quadraturer   r   r   r   r	   r
   r   r   r/   r5   rC   rG   r\   ra   rz   r   r   r   r   r   r   r   r   r   r   r   r   <module>r      s   " " " " " " " "E E E E E E E E E E E E E E E E E E E E!# !# !#H	: 	: 	:1% 1% 1%h	; 	; 	;/$ /$ /$d	6 	6 	6_& _& _&D; ; ;,/# /# /#d	9 	9 	9/# /# /#d	: 	: 	:_$ _$ _$D: : :,+# +# +#\	: 	: 	: 	: 	:r   