Ë
    7^(hÏM  ã                   óœ   — 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)é    )ÚSÚRational)Úgauss_legendreÚgauss_laguerreÚgauss_hermiteÚgauss_gen_laguerreÚgauss_chebyshev_tÚgauss_chebyshev_uÚgauss_jacobiÚgauss_lobattoc                  óÈ  — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚t        d	d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d
¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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 )Né   é   Ú0ú2.0000000000000000é   z-0.57735026918962576z0.57735026918962576ú1.0000000000000000é   )z-0.77459666924148338r   z0.77459666924148338)ú0.55555555555555556z0.88888888888888889r   é   )z-0.86113631159405258z-0.33998104358485626z0.33998104358485626z0.86113631159405258)ú0.34785484513745386ú0.65214515486254614r   r   ©r   Ústr©ÚxÚwÚrs      úc/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/integrals/tests/test_quadrature.pyÚtest_legendrer       s¢  € Ü˜!˜RÓ �D€A€qØÖ�qŒC��FÒ 3 %Ò'Ð'Ð'ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜!˜RÓ �D€A€qØÖ�qŒC��FÒØ"Ø!ð##ò #ð #ð #ð Ö�qŒC��FÒØ Ø ð#"ò "ð "ð "ô ˜!˜RÓ �D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð Ö�qŒC��FÒò ##ò #ð #ð #ô
 ˜!˜RÓ �D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð
 Ö�qŒC��FÒò ##ò #ð #ñ #ùò7 ùÚùò ùò ùò
 ùò ùò ùò
 s.   ”D<³EÁ!EÂEÂ0EÃEÃ?EÄEc                  ó¶   — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚y c c}w c c}w )Nr   é(   )z+-0.7745966692414833770358530799564799221666r   z*0.7745966692414833770358530799564799221666)ú*0.5555555555555555555555555555555555555556z*0.8888888888888888888888888888888888888889r#   r   r   s      r   Útest_legendre_preciser$   ,   sj   € Ü˜!˜RÓ �D€A€qØÖ�qŒC��FÒò #:ò :ð :ð :ð Ö�qŒC��FÒò #:ò :ð :ñ :ùò	 ùò ó
   ”A´Ac                  óz  — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚t        d	d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d
¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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0.00053929470556132745é   )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   Útest_laguerrer)   8   s  € Ü˜!˜RÓ �D€A€qØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜!˜RÓ �D€A€qØÖ�qŒC��FÒØ!Ø ð#"ò "ð "ð "ð Ö�qŒC��FÒØ!Ø!ð##ò #ð #ð #ô ˜!˜RÓ �D€A€qØÖ�qŒC��FÒò #ò ð ð ð
 Ö�qŒC��FÒò #ò ð ð ô ˜!˜RÓ �D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð
 Ö�qŒC��FÒò #&ò &ð &ð &ô ˜!˜RÓ �D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð Ö�qŒC��FÒò #%ò %ð %ñ %ùòU ùÚùò ùò ùò
 ùò
 ùò ùò
 ùò ùò ó:   ”F³FÁ!FÂFÂ0FÃF$Ã?F)ÄF.ÅF3Å.F8c                  ó¶   — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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   Útest_laguerre_preciser,   l   sj   € Ü˜!˜RÓ �D€A€qØÖ�qŒC��FÒò #9ò 9ð 9ð 9ð Ö�qŒC��FÒò #;ò ;ð ;ñ ;ùò	 ùò r%   c                  óz  — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚t        d	d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d
¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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   ú1.7724538509055160r   ú-0.70710678118654752ú0.70710678118654752z0.88622692545275801r   )z-1.2247448713915890r   z1.2247448713915890)ú0.29540897515091934z1.1816359006036774r1   r   )z-1.6506801238857846z-0.52464762327529032z0.52464762327529032z1.6506801238857846)ú0.081312835447245177ú0.80491409000551284r3   r2   r'   )z-2.0201828704560856z-0.95857246461381851r   z0.95857246461381851z2.0201828704560856)ú0.019953242059045913ú0.39361932315224116z0.94530872048294188r5   r4   ©r   r   r   s      r   Útest_hermiter7   x   s  € Ü˜˜BÓ�D€A€qØÖ�qŒC��FÒ 3 %Ò'Ð'Ð'ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜˜BÓ�D€A€qØÖ�qŒC��FÒØ"Ø!ð##ò #ð #ð #ð Ö�qŒC��FÒØ!Ø!ð##ò #ð #ð #ô ˜˜BÓ�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð Ö�qŒC��FÒò ##ò #ð #ð #ô
 ˜˜BÓ�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð
 Ö�qŒC��FÒò #$ò $ð $ð $ô ˜˜BÓ�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð Ö�qŒC��FÒò #$ò $ð $ñ $ùòQ ùÚùò ùò ùò
 ùò ùò ùò
 ùò ùò r*   c                  ó¶   — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚y c c}w c c}w )Nr   r"   )z*-1.224744871391589049098642037352945695983r   z)1.224744871391589049098642037352945695983)ú*0.2954089751509193378830279138901908637996z)1.181635900603677351532111655560763455198r9   r6   r   s      r   Útest_hermite_preciser:   ª   sj   € Ü˜˜BÓ�D€A€qØÖ�qŒC��FÒò #5ò 5ð 5ð 5ð Ö�qŒC��FÒò #6ò 6ð 6ñ 6ùò	 ùò r%   c                  óh  — t        dt        dd«      d«      \  } }| D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚t        dt        dd«      d«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}d	d
gk(  sJ ‚t        dt        dd«      d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dt        dd«      d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dt        dd«      d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        ddd«      \  } }| D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚t        ddd«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚t        ddd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        ddd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        ddd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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   éÿÿÿÿr   r   ú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   Útest_gen_laguerrer?   ¶   sO  € Ü˜a¤¨"¨a£°"Ó5�D€A€qØÖ�qŒC��FÒÐ#8Ð"9Ò9Ð9Ð9ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜a¤¨"¨a£°"Ó5�D€A€qØÖ�qŒC��FÒØ!Ø ð#"ò "ð "ð "ð Ö�qŒC��FÒØ Ø!ð##ò #ð #ð #ô ˜a¤¨"¨a£°"Ó5�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð Ö�qŒC��FÒò #%ò %ð %ð %ô
 ˜a¤¨"¨a£°"Ó5�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð
 Ö�qŒC��FÒò #&ò &ð &ð &ô ˜a¤¨"¨a£°"Ó5�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð Ö�qŒC��FÒò #%ò %ð %ð %ô ˜a  BÓ'�D€A€qØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜a  BÓ'�D€A€qØÖ�qŒC��FÒØ Ø ð#"ò "ð "ð "ð Ö�qŒC��FÒØ Ø!ð##ò #ð #ð #ô ˜a  BÓ'�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð Ö�qŒC��FÒò #$ò $ð $ð $ô
 ˜a  BÓ'�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð
 Ö�qŒC��FÒò #%ò %ð %ð %ô ˜a  BÓ'�D€A€qØÖ�qŒC��FÒò #"ò "ð "ð "ð Ö�qŒC��FÒò #&ò &ð &ñ &ùòq ùÚùò ùò ùò
 ùò ùò ùò
 ùò ùò ùò ùÚùò ùò ùò
 ùò ùò ùò
 ùò ùò sv   ŸM¾MÁ7MÂMÃM$Ã1M)Ä+M.ÅM3ÆM8Æ%M=ÇNÇ4NÈ#NÉNÉ3NÊNËN Ë#N%ÌN*Ì3N/c                  ó€  — t        dt        dd«      d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        ddd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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   Útest_gen_laguerre_preciserA     sÞ   € Ü˜a¤¨"¨a£°"Ó5�D€A€qØÖ�qŒC��FÒò #9ò 9ð 9ð 9ð Ö�qŒC��FÒò #<ò <ð <ð <ô
 ˜a  BÓ'�D€A€qØÖ�qŒC��FÒò #9ò 9ð 9ð 9ð Ö�qŒC��FÒò #;ò ;ð ;ñ ;ùò ùò ùò ùò s   ŸB,¿B1Á/B6ÂB;c                  óz  — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚t        d	d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d
¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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   ú3.1415926535897932r   r0   r/   ú1.5707963267948966r   )ú0.86602540378443865r   ú-0.86602540378443865)ú1.0471975511965977rG   rG   r   )z0.92387953251128676z0.38268343236508977z-0.38268343236508977z-0.92387953251128676)ú0.78539816339744831rH   rH   rH   r'   )z0.95105651629515357z0.58778525229247313r   z-0.58778525229247313z-0.95105651629515357)ú0.62831853071795865rI   rI   rI   rI   ©r	   r   r   s      r   Útest_chebyshev_trK   .  s  € Ü˜Q Ó#�D€A€qØÖ�qŒC��FÒ 3 %Ò'Ð'Ð'ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜Q Ó#�D€A€qØÖ�qŒC��FÒØ!Ø"ð#$ò $ð $ð $ð Ö�qŒC��FÒØ Ø ð#"ò "ð "ð "ô ˜Q Ó#�D€A€qØÖ�qŒC��FÒò #$ò $ð $ð $ð Ö�qŒC��FÒò #"ò "ð "ð "ô
 ˜Q Ó#�D€A€qØÖ�qŒC��FÒò #$ò $ð $ð $ð
 Ö�qŒC��FÒò ##ò #ð #ð #ô ˜Q Ó#�D€A€qØÖ�qŒC��FÒò #$ò $ð $ð $ð Ö�qŒC��FÒò ##ò #ð #ñ #ùòQ ùÚùò ùò ùò
 ùò ùò ùò
 ùò ùò r*   c                  ó¶   — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚y c c}w c c}w )Nr   r"   )z*0.8660254037844386467637231707529361834714r   z+-0.8660254037844386467637231707529361834714)ú)1.047197551196597746154214461093167628066rM   rM   rJ   r   s      r   Útest_chebyshev_t_preciserN   `  sj   € Ü˜Q Ó#�D€A€qØÖ�qŒC��FÒò #;ò ;ð ;ð ;ð Ö�qŒC��FÒò #9ò 9ð 9ñ 9ùò	 ùò r%   c                  óz  — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}dgk(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚t        d	d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d
¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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=   ú-0.50000000000000000rH   r   )r0   r   r/   )ú0.39269908169872415rH   rQ   r   )ú0.80901699437494742z0.30901699437494742ú-0.30901699437494742z-0.80901699437494742)ú0.21707871342270599ú0.56831944997474231rU   rT   r'   )rE   r=   r   rP   rF   )ú0.13089969389957472rQ   z0.52359877559829887rQ   rV   ©r
   r   r   s      r   Útest_chebyshev_urX   l  s  € Ü˜Q Ó#�D€A€qØÖ�qŒC��FÒ 3 %Ò'Ð'Ð'ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜Q Ó#�D€A€qØÖ�qŒC��FÒØ!Ø"ð#$ò $ð $ð $ð Ö�qŒC��FÒØ!Ø!ð##ò #ð #ð #ô ˜Q Ó#�D€A€qØÖ�qŒC��FÒò #$ò $ð $ð $ð Ö�qŒC��FÒò ##ò #ð #ð #ô
 ˜Q Ó#�D€A€qØÖ�qŒC��FÒò #$ò $ð $ð $ð
 Ö�qŒC��FÒò ##ò #ð #ð #ô ˜Q Ó#�D€A€qØÖ�qŒC��FÒò #$ò $ð $ð $ð Ö�qŒC��FÒò ##ò #ð #ñ #ùòQ ùÚùò ùò ùò
 ùò ùò ùò
 ùò ùò r*   c                  ó¶   — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚y c c}w c c}w )Nr   r"   )z*0.7071067811865475244008443621048490392848r   z+-0.7071067811865475244008443621048490392848)ú*0.3926990816987241548078304229099378605246z*0.7853981633974483096156608458198757210493rZ   rW   r   s      r   Útest_chebyshev_u_preciser[   ž  sj   € Ü˜Q Ó#�D€A€qØÖ�qŒC��FÒò #;ò ;ð ;ð ;ð Ö�qŒC��FÒò #:ò :ð :ñ :ùò	 ùò r%   c                  ó  — t        dt        dd«      t        j                  d«      \  } }| D �cg c]  }t	        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}dgk(  sJ ‚t        dt        dd«      t        j                  d«      \  } }| D �cg c]  }t	        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}d	d
gk(  sJ ‚t        dt        dd«      t        j                  d«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚t        dt        dd«      t        j                  d«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚t        dt        dd«      t        j                  d«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚t        dddd«      \  } }| D �cg c]  }t	        |«      ‘Œ c}dgk(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}dgk(  sJ ‚t        dddd«      \  } }| D �cg c]  }t	        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}ddgk(  sJ ‚t        dddd«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚t        dddd«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚t        dddd«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ 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   ÚHalfr   r   s      r   Útest_jacobir_   ª  sw  € Ü˜œ8 B¨›?¬A¯F©F°BÓ7�D€A€qØÖ�qŒC��FÒÐ#8Ð"9Ò9Ð9Ð9ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜œ8 B¨›?¬A¯F©F°BÓ7�D€A€qØÖ�qŒC��FÒØ"Ø!ð##ò #ð #ð #ð Ö�qŒC��FÒØ!Ø ð#"ò "ð "ð "ô ˜œ8 B¨›?¬A¯F©F°BÓ7�D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð Ö�qŒC��FÒò #"ò "ð "ð "ô
 ˜œ8 B¨›?¬A¯F©F°BÓ7�D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð
 Ö�qŒC��FÒò #"ò "ð "ð "ô ˜œ8 B¨›?¬A¯F©F°BÓ7�D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð Ö�qŒC��FÒò #"ò "ð "ð "ô ˜˜1˜a Ó$�D€A€qØÖ�qŒC��FÒÐ#8Ð"9Ò9Ð9Ð9ØÖ�qŒC��FÒÐ#7Ð"8Ò8Ð8Ð8ä˜˜1˜a Ó$�D€A€qØÖ�qŒC��FÒØ"Ø!ð##ò #ð #ð #ð Ö�qŒC��FÒØ!Ø!ð##ò #ð #ð #ô ˜˜1˜a Ó$�D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð Ö�qŒC��FÒò ##ò #ð #ð #ô
 ˜˜1˜a Ó$�D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð
 Ö�qŒC��FÒò ##ò #ð #ð #ô ˜˜1˜a Ó$�D€A€qØÖ�qŒC��FÒò ##ò #ð #ð #ð Ö�qŒC��FÒò #$ò $ð $ñ $ùòq ùÚùò ùò ùò
 ùò ùò ùò
 ùò ùò ùò ùÚùò ùò ùò
 ùò ùò ùò
 ùò ùò sw   ®N ÁN%ÂN*Â5N/Ã>N4ÄN9Å'N>ÆOÇOÇ0OÈ!OÉ OÉ0OÊO!ËO&Ë!O+ÌO0Ì2O5Í#O:ÎO?c                  ó   — t        dt        dd«      t        j                  d«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚t        dddd«      \  } }| D �cg c]  }t	        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t	        |«      ‘Œ 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   Útest_jacobi_precisera     sæ   € Ü˜œ8 B¨›?¬A¯F©F°BÓ7�D€A€qØÖ�qŒC��FÒò #:ò :ð :ð :ð Ö�qŒC��FÒò #9ò 9ð 9ð 9ô
 ˜˜1˜a Ó$�D€A€qØÖ�qŒC��FÒò #:ò :ð :ð :ð Ö�qŒC��FÒò #:ò :ð :ñ :ùò ùò ùò ùò s   ®B<ÁCÁ?CÂCc                  óÌ  — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}ddgk(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        d	d«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d
¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ 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   ú-1Ú1r   r   ©rc   r   rd   )ú0.33333333333333333z1.3333333333333333rf   r   )rc   z-0.44721359549995794z0.44721359549995794rd   )ú0.16666666666666667ú0.83333333333333333rh   rg   r'   )rc   z-0.65465367070797714r   z0.65465367070797714rd   )ú0.10000000000000000ú0.54444444444444444z0.71111111111111111rj   ri   ©r   r   r   s      r   Útest_lobattorl   "  sµ  € Ü˜˜BÓ�D€A€qØÖ�qŒC��FÒØØð#ò ð ð ð Ö�qŒC��FÒØ Ø ð#"ò "ð "ð "ô ˜˜BÓ�D€A€qØÖ�qŒC��FÒò #ò ð ð ð Ö�qŒC��FÒò ##ò #ð #ð #ô
 ˜˜BÓ�D€A€qØÖ�qŒC��FÒò #ò ð ð ð
 Ö�qŒC��FÒò ##ò #ð #ð #ô ˜˜BÓ�D€A€qØÖ�qŒC��FÒò #ò ð ð ð Ö�qŒC��FÒò ##ò #ð #ñ #ùòI ùò ùò
 ùò ùò ùò
 ùò ùò s.   ”D>´EÁ#EÂEÂ2EÃEÄEÄ!E!c                  ó¶   — t        dd«      \  } }| D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚|D �cg c]  }t        |«      ‘Œ c}g d¢k(  sJ ‚y c c}w c c}w )Nr   r"   re   )ú*0.3333333333333333333333333333333333333333z)1.333333333333333333333333333333333333333rn   rk   r   s      r   Útest_lobatto_precisero   P  sj   € Ü˜˜BÓ�D€A€qØÖ�qŒC��FÒò #ò ð ð ð Ö�qŒC��FÒò #:ò :ð :ñ :ùò	 ùò r%   N)Ú
sympy.corer   r   Ú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   © ó    r   ú<module>rt      st   ðß "÷E÷ Eó Eò!#òH	:ò1%òh	;ò/$òd	6ò_&òD;ò,/#òd	9ò/#òd	:ò_$òD:ò,+#ó\	:rs   