
    sgM                         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y)    )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 cg c]  }t        |       c}dgk(  sJ |D cg c]  }t        |       c}dgk(  sJ t        dd      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}ddgk(  sJ t        d	d      \  } }| D cg c]  }t        |       c}g d
k(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )N      02.0000000000000000   z-0.57735026918962576z0.577350269189625761.0000000000000000   )z-0.77459666924148338r   z0.77459666924148338)0.55555555555555556z0.88888888888888889r      )z-0.86113631159405258z-0.33998104358485626z0.33998104358485626z0.86113631159405258)0.347854845137453860.65214515486254614r   r   r   strxwrs      X/var/www/html/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_quadrature.pytest_legendrer       s   !R DAqqCF3%'''qCF#7"8888!R DAqqCF"!## # # # qCF  #" " " " !R DAqqCF ## # # # qCF ## # # #
 !R DAqqCF ## # # #
 qCF ## # # #7   
   
 s.   D<E!EE0EE?EEc                      t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w )Nr   (   )z+-0.7745966692414833770358530799564799221666r   z*0.7745966692414833770358530799564799221666)*0.5555555555555555555555555555555555555556z*0.8888888888888888888888888888888888888889r#   r   r   s      r   test_legendre_preciser$   ,   sj    !R DAqqCF #: : : : qCF #: : : :	  
   AAc                  z   t        dd      \  } }| D cg c]  }t        |       c}dgk(  sJ |D cg c]  }t        |       c}dgk(  sJ t        dd      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}ddgk(  sJ t        d	d      \  } }| D cg c]  }t        |       c}g d
k(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )Nr   r   r   r   z0.58578643762690495z3.4142135623730950z0.85355339059327376z0.14644660940672624r   )z0.41577455678347908z2.2942803602790417z6.2899450829374792)z0.71109300992917302z0.27851773356924085z0.010389256501586136r   )z0.32254768961939231z1.7457611011583466z4.5366202969211280z9.3950709123011331)z0.60315410434163360z0.35741869243779969z0.038887908515005384z0.00053929470556132745   )z0.26356031971814091z1.4134030591065168z3.5964257710407221z7.0858100058588376z12.640800844275783)z0.52175561058280865z0.39866681108317593z0.075942449681707595z0.0036117586799220485z2.3369972385776228e-5r   r   r   s      r   test_laguerrer)   8   s   !R DAqqCF#7"8888qCF#7"8888!R DAqqCF! #" " " " qCF!!## # # # !R DAqqCF #   
 qCF #    !R DAqqCF #" " " "
 qCF #& & & & !R DAqqCF #" " " " qCF #% % % %U   
 
  
   :   FF!FF0FF$?F)F.F3.F8c                      t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w )Nr   r"   )z*0.4157745567834790833115338731282744735466z)2.294280360279041719822050361359593868960z)6.289945082937479196866415765512131657493)z*0.7110930099291730154495901911425944313094z*0.2785177335692408488014448884567264810349z+0.01038925650158613574896492040067908765572r(   r   s      r   test_laguerre_preciser,   l   sj    !R DAqqCF #9 9 9 9 qCF #; ; ; ;	  r%   c                  z   t        dd      \  } }| D cg c]  }t        |       c}dgk(  sJ |D cg c]  }t        |       c}dgk(  sJ t        dd      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}ddgk(  sJ t        d	d      \  } }| D cg c]  }t        |       c}g d
k(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )Nr   r   r   1.7724538509055160r   -0.707106781186547520.70710678118654752z0.88622692545275801r   )z-1.2247448713915890r   z1.2247448713915890)0.29540897515091934z1.1816359006036774r1   r   )z-1.6506801238857846z-0.52464762327529032z0.52464762327529032z1.6506801238857846)0.0813128354472451770.80491409000551284r3   r2   r'   )z-2.0201828704560856z-0.95857246461381851r   z0.95857246461381851z2.0201828704560856)0.0199532420590459130.39361932315224116z0.94530872048294188r5   r4   r   r   r   s      r   test_hermiter7   x   s   BDAqqCF3%'''qCF#7"8888BDAqqCF"!## # # # qCF!!## # # # BDAqqCF #" " " " qCF ## # # #
 BDAqqCF #" " " "
 qCF #$ $ $ $ BDAqqCF #" " " " qCF #$ $ $ $Q   
   
   r*   c                      t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w )Nr   r"   )z*-1.224744871391589049098642037352945695983r   z)1.224744871391589049098642037352945695983)*0.2954089751509193378830279138901908637996z)1.181635900603677351532111655560763455198r9   r6   r   s      r   test_hermite_preciser:      sj    BDAqqCF #5 5 5 5 qCF #6 6 6 6	  r%   c                  h   t        dt        dd      d      \  } }| D cg c]  }t        |       c}dgk(  sJ |D cg c]  }t        |       c}dgk(  sJ t        dt        dd      d      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}d	d
gk(  sJ t        dt        dd      d      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dt        dd      d      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dt        dd      d      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        ddd      \  } }| D cg c]  }t        |       c}dgk(  sJ |D cg c]  }t        |       c}dgk(  sJ t        ddd      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}ddgk(  sJ t        ddd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        ddd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        ddd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )Nr   r   r   0.50000000000000000r.   z0.27525512860841095z2.7247448713915890z1.6098281800110257z0.16262567089449035r   )z0.19016350919348813z1.7844927485432516z5.5253437422632603)z1.4492591904487850z0.31413464064571329z0.0090600198110176913r   )z0.14530352150331709z1.3390972881263614z3.9269635013582872z8.5886356890120343)z1.3222940251164826z0.41560465162978376z0.034155966014826951z0.00039920814442273524r'   )z0.11758132021177814z1.0745620124369040z3.0859374437175500z6.4147297336620305z11.807189489971737)z1.2217252674706516z0.48027722216462937z0.067748788910962126z0.0026872914935624654z1.5280865710465241e-5z3.0000000000000000r   z6.0000000000000000z1.5000000000000000)z1.5173870806774125z4.3115831337195203z9.1710297856030672)z1.0374949614904253z0.90575000470306537z0.056755033806509347)z1.2267632635003021z3.4125073586969460z6.9026926058516134z12.458036771951139)z0.72552499769865438z1.0634242919791946z0.20669613102835355z0.0043545792937974889)z1.0311091440933816z2.8372128239538217z5.6202942725987079z9.6829098376640271z15.828473921690062)z0.52091739683509184z1.0667059331592211z0.38354972366693113z0.028564233532974658z0.00026271280578124935r   r   r   r   s      r   test_gen_laguerrer?      sO   a"a"5DAqqCF#8"9999qCF#7"8888a"a"5DAqqCF! #" " " " qCF !## # # # a"a"5DAqqCF #" " " " qCF #% % % %
 a"a"5DAqqCF #" " " "
 qCF #& & & & a"a"5DAqqCF #" " " " qCF #% % % % aB'DAqqCF#7"8888qCF#7"8888aB'DAqqCF  #" " " " qCF !## # # # aB'DAqqCF #" " " " qCF #$ $ $ $
 aB'DAqqCF #" " " "
 qCF #% % % % aB'DAqqCF #" " " " qCF #& & & &q   
   
      
   
   sv   MM7MMM$1M)+M.M3M8%M=N4N#NN3NNN #N%N*3N/c                     t        dt        dd      d      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        ddd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w )	Nr   r<   r   r"   )z*0.1901635091934881328718554276203028970878z)1.784492748543251591186722461957367638500z)5.525343742263260275941422110422329464413)z)1.449259190448785048183829411195134343108z*0.3141346406457132878326231270167565378246z,0.009060019811017691281714945129254301865020)z)1.517387080677412495020323111016672547482z)4.311583133719520302881184669723530562299z)9.171029785603067202098492219259796890218)z)1.037494961490425285817554606541269153041z*0.9057500047030653669269785048806009945254z+0.05675503380650934725546688857812985243312r>   r   s      r   test_gen_laguerre_preciserA     s    a"a"5DAqqCF #9 9 9 9 qCF #< < < <
 aB'DAqqCF #9 9 9 9 qCF #; ; ; ;    s   B,B1/B6B;c                  z   t        dd      \  } }| D cg c]  }t        |       c}dgk(  sJ |D cg c]  }t        |       c}dgk(  sJ t        dd      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}ddgk(  sJ t        d	d      \  } }| D cg c]  }t        |       c}g d
k(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )Nr   r   r   3.1415926535897932r   r0   r/   1.5707963267948966r   )0.86602540378443865r   -0.86602540378443865)1.0471975511965977rG   rG   r   )z0.92387953251128676z0.38268343236508977z-0.38268343236508977z-0.92387953251128676)0.78539816339744831rH   rH   rH   r'   )z0.95105651629515357z0.58778525229247313r   z-0.58778525229247313z-0.95105651629515357)0.62831853071795865rI   rI   rI   rI   r	   r   r   s      r   test_chebyshev_trK   .  s   Q#DAqqCF3%'''qCF#7"8888Q#DAqqCF!"#$ $ $ $ qCF  #" " " " Q#DAqqCF #$ $ $ $ qCF #" " " "
 Q#DAqqCF #$ $ $ $
 qCF ## # # # Q#DAqqCF #$ $ $ $ qCF ## # # #Q   
   
   r*   c                      t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w )Nr   r"   )z*0.8660254037844386467637231707529361834714r   z+-0.8660254037844386467637231707529361834714))1.047197551196597746154214461093167628066rM   rM   rJ   r   s      r   test_chebyshev_t_preciserN   `  sj    Q#DAqqCF #; ; ; ; qCF #9 9 9 9	  r%   c                  z   t        dd      \  } }| D cg c]  }t        |       c}dgk(  sJ |D cg c]  }t        |       c}dgk(  sJ t        dd      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}ddgk(  sJ t        d	d      \  } }| D cg c]  }t        |       c}g d
k(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )Nr   r   r   rD   r   r=   -0.50000000000000000rH   r   )r0   r   r/   )0.39269908169872415rH   rQ   r   )0.80901699437494742z0.30901699437494742-0.30901699437494742z-0.80901699437494742)0.217078713422705990.56831944997474231rU   rT   r'   )rE   r=   r   rP   rF   )0.13089969389957472rQ   z0.52359877559829887rQ   rV   r
   r   r   s      r   test_chebyshev_urX   l  s   Q#DAqqCF3%'''qCF#7"8888Q#DAqqCF!"#$ $ $ $ qCF!!## # # # Q#DAqqCF #$ $ $ $ qCF ## # # #
 Q#DAqqCF #$ $ $ $
 qCF ## # # # Q#DAqqCF #$ $ $ $ qCF ## # # #Q   
   
   r*   c                      t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w )Nr   r"   )z*0.7071067811865475244008443621048490392848r   z+-0.7071067811865475244008443621048490392848)*0.3926990816987241548078304229099378605246z*0.7853981633974483096156608458198757210493rZ   rW   r   s      r   test_chebyshev_u_preciser[     sj    Q#DAqqCF #; ; ; ; qCF #: : : :	  r%   c                     t        dt        dd      t        j                  d      \  } }| D cg c]  }t	        |       c}dgk(  sJ |D cg c]  }t	        |       c}dgk(  sJ t        dt        dd      t        j                  d      \  } }| D cg c]  }t	        |       c}ddgk(  sJ |D cg c]  }t	        |       c}d	d
gk(  sJ t        dt        dd      t        j                  d      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ t        dt        dd      t        j                  d      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ t        dt        dd      t        j                  d      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ t        dddd      \  } }| D cg c]  }t	        |       c}dgk(  sJ |D cg c]  }t	        |       c}dgk(  sJ t        dddd      \  } }| D cg c]  }t	        |       c}ddgk(  sJ |D cg c]  }t	        |       c}ddgk(  sJ t        dddd      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ t        dddd      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ t        dddd      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w ) Nr   r<   r   r   r=   rC   rS   rR   z0.86831485369082398z2.2732777998989693r   )z-0.62348980185873353z0.22252093395631440z0.90096886790241913)z0.33795476356635433z1.0973322242791115z1.7063056657443274r   )z-0.76604444311897804z-0.17364817766693035r=   z0.93969262078590838)z0.16333179083642836z0.57690240318269103rG   z1.3541609083740761r'   )z-0.84125353283118117z-0.41541501300188643z0.14231483827328514z0.65486073394528506z0.95949297361449739)z0.090675770007435372z0.33391416373675607z0.65248870981926643z0.94525424081394926z1.1192597692123861z0.14285714285714286z1.0666666666666667z-0.24025307335204215z0.46247529557426437z0.48514624517838660z0.58152042148828007)z-0.46115870378089762z0.10438533038323902z0.62950064612493132)z0.17937613502213266z0.61595640991147154z0.27133412173306246)z-0.59903470850824782z-0.14761105199952565z0.32554377081188859z0.72879429738819258)z0.067809641836772187z0.38956404952032481z0.47995970868024150z0.12933326662932816)z-0.69045775012676106z-0.32651993134900065z0.082337849552034905z0.47517887061283164z0.79279429464422850)z0.027410178066337099z0.21291786060364828z0.43908437944395081z0.32220656547221822z0.065047683080512268r   r   r   Halfr   r   s      r   test_jacobir_     sw   8B?AFFB7DAqqCF#8"9999qCF#7"88888B?AFFB7DAqqCF"!## # # # qCF! #" " " " 8B?AFFB7DAqqCF ## # # # qCF #" " " "
 8B?AFFB7DAqqCF ## # # #
 qCF #" " " " 8B?AFFB7DAqqCF ## # # # qCF #" " " " 1a$DAqqCF#8"9999qCF#7"88881a$DAqqCF"!## # # # qCF!!## # # # 1a$DAqqCF ## # # # qCF ## # # #
 1a$DAqqCF ## # # #
 qCF ## # # # 1a$DAqqCF ## # # # qCF #$ $ $ $q   
   
      
   
   sw   N N%N*5N/>N4N9'N>OO0O!O O0OO!O&!O+O02O5#O:O?c                     t        dt        dd      t        j                  d      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ t        dddd      \  } }| D cg c]  }t	        |       c}g dk(  sJ |D cg c]  }t	        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w )	Nr   r<   r   r"   )z+-0.6234898018587335305250048840042398106323z*0.2225209339563144042889025644967947594664z*0.9009688679024191262361023195074450511659)z*0.3379547635663543330553835737094171534907z)1.097332224279111467485302294320899710461z)1.706305665744327437921957515249186020246)z+-0.4611587037808976179121958105554375981274z*0.1043853303832390210914918407615869143233z*0.6295006461249313240934312425211234110769)z*0.1793761350221326596137764371503859752628z*0.6159564099114715430909548532229749439714z*0.2713341217330624639619353762933057474325r]   r   s      r   test_jacobi_precisera     s    8B?AFFB7DAqqCF #: : : : qCF #9 9 9 9
 1a$DAqqCF #: : : : qCF #: : : :    s   B<C?CCc                     t        dd      \  } }| D cg c]  }t        |       c}ddgk(  sJ |D cg c]  }t        |       c}ddgk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ t        d	d      \  } }| D cg c]  }t        |       c}g d
k(  sJ |D cg c]  }t        |       c}g dk(  sJ t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )Nr   r   -11r   r   rc   r   rd   )0.33333333333333333z1.3333333333333333rf   r   )rc   z-0.44721359549995794z0.44721359549995794rd   )0.166666666666666670.83333333333333333rh   rg   r'   )rc   z-0.65465367070797714r   z0.65465367070797714rd   )0.100000000000000000.54444444444444444z0.71111111111111111rj   ri   r   r   r   s      r   test_lobattorl   "  s   BDAqqCF#    qCF  #" " " " BDAqqCF #    qCF ## # # #
 BDAqqCF #   
 qCF ## # # # BDAqqCF #    qCF ## # # #I  
   
   s.   D>E#EE2EEE!E!c                      t        dd      \  } }| D cg c]  }t        |       c}g dk(  sJ |D cg c]  }t        |       c}g dk(  sJ y c c}w c c}w )Nr   r"   re   )*0.3333333333333333333333333333333333333333z)1.333333333333333333333333333333333333333rn   rk   r   s      r   test_lobatto_precisero   P  sj    BDAqqCF #    qCF #: : : :	  r%   N)
sympy.corer   r   sympy.integrals.quadraturer   r   r   r   r	   r
   r   r   r    r$   r)   r,   r7   r:   r?   rA   rK   rN   rX   r[   r_   ra   rl   ro        r   <module>rt      st    "E E E!#H	:1%h	;/$d	6_&D;,/#d	9/#d	:_$D:,+#\	:rs   