U
    ZÊ¹j#w ã                   @   sn   d Z ddlmZ ddlmZ ddlmZmZ ddlm	Z	 ddl
mZ ddlmZ edƒZeG d	d
„ d
ƒƒZdS )a  
Solving solvable quintics - An implementation of DS Dummit's paper

Paper :
https://www.ams.org/journals/mcom/1991-57-195/S0025-5718-1991-1079014-X/S0025-5718-1991-1079014-X.pdf

Mathematica notebook:
http://www.emba.uvm.edu/~ddummit/quintics/quintics.nb

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d„ ƒZ	edd„ ƒZ
edd„ ƒZdd„ Zdd„ Zdd„ Zdd„ Zedd„ ƒZdS )ÚPolyQuinticz'Special functions for solvable quinticsc                 C   s   |  ¡ \}}| _| _| _| _tddƒtdƒd  tttdƒd tddƒ ƒ  | _tdƒ d tddƒ tttdƒ d tddƒ ƒ  | _	tdƒ d tddƒ tttdƒ d tddƒ ƒ  | _
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    6::zPolyQuintic.__init__c                 C   s‚  | j | j| j| jf\}}}}|d d| |d  |  |d |d  |d   d|d  |d  |d   d|d  |d   d	|d  |d  |d   d
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  éô  éq  é	   éˆ   i�  é2   éZ   ix  é   é(   é   )r   r   r   r   r	   r   )r   r   r   r   r   Úf20r   r   r   rF       s    ÿ ÿ ÿ ÿ ÿ ÿ bzPolyQuintic.f20c              
   C   sðá  | j | j| j| jf\}}}}g ddddddgddddddgddddddgddddddgf}d|d  |d  d|d  |d   d| |d   d	|d
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  | |d   dª|d  |d  |d   d«|d  |d  |d   d¬|d  | |d   d­|d  |d  |d   d®|d  |d   d¯|d  | |d   d°| |d  |d   d…|d  | |d   d'|d
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|d  |d  �d|d  |�d   di|�d   �d|d  |d  |  �d|d  |d  |  �d| |�d  |  �d|d
  |d  |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  |d  |d   �d| |d  |d   �d|d  | |d   �d|d
  |d  |d   �d|d  |d  |d   �d|d  |d  |d   �d |d  | |d   �d!|d  |d  |d   �d"|d  |d  |d   �d#|d  |d   �d$|d  | |d   �d%|d  |d  |d   �d&| |d  |d   �d'|d  | |d
   �d(|d  |d  |d
   d8|d  | |d   �d)|d  |d   �d*|d
  |d
  |  �d+|d  |d  |  �d,|d  |�d-  |  �d.|d  |d  | |  �d/|d  |d
  | |  �d0|d  |d  | |  �d1|�d-  | |  �d2|d  |d  |d  |  �d3|d  |d  |d  |  �d4|d  |d
  |d  |  �d5| |d  |d  |  �d6|d  |d  |d  |  �d7|d
  |d  |d  |  �d8|d  |d  |d  |  �d9|d  |d
  |d  |  dù|�d-  |d  |  �d:|d  |d  |d  |  �d;|d  |d  |d  |  �d<|d  |d  |d  |  �d=|d
  |d  |  �d>|d  |d  |  �d?|d  |d  |d  |  �d@|d  |d  |d  |  �dA| |d  |d  |  �dB|d
  |d  |  �dC|d  |d  |d  |  �dD|d  |d  |d  |  �dE|d  |d  |  �dF|d  |d  |d  |  �dG|d  |d  |  �dH|d  |d
  |  �dI| |d  |d
  |  �dJ|d  |d  |  �dK|d  |d  |d   �dL|d  |d  |d   �dM|d  |d  |d   �dN| |d  |d   �dO|d  |d  | |d   �dP|d
  |d  | |d   �dQ|d  |d  | |d   �dR|d  |d  | |d   �dS|�d-  | |d  |d   �dT|d  |d  |d  |d   �dU|d  |d  |d  |d   �dV|d  |d  |d  |d   �dW|d  |d  |d   �dX|d  | |d  |d   �dY|d  |d  |d  |d   �dZ|d  |d  |d  |d   �d[| |d  |d  |d   �d\|d
  | |d  |d   �d]|d  |d  |d  |d   �d^|d  |d  |d  |d   �d_|d  | |d  |d   �d`|d  |d  |d  |d   �da|d  |d  |d   �db|d  | |d  |d   �dc| |d  |d  |d   �dd|d  | |d  |d   �de| |d
  |d   �df|�d-  |d  |d   �dg|d  |d  |d   �dh|d  |d  |d   �di|d  |d
  |d   �dj|d  |d   �dk|�d  | |d   �dl|d  |d  | |d   �dm|d  |d  | |d   �dn|d  |d  | |d   �do| |d
  | |d   �dp|d  |d  |d   �dq|d
  |d  |d  |d   �dr|d  |d  |d  |d   �ds|d  |d  |d  |d   �dt|d  |d  |d   �du|d  |d  |d  |d   �dv|d  |d  |d  |d   �dw|d  |d  |d   �dx|d  |d  |d   �dy|d  |d  |d  |d   �dz| |d  |d  |d   �d{|d  |d  |d   �d||d  |d  |d  |d   �d}|d  |d  |d   �d~|d  |d  |d   �d| |d  |d   �d€|d  | |d   �d�|d
  |d  |d   �d‚|d  |d  |d   �dƒ|d  |d  |d   �d„|d  | | |d   �d…|d  |d  | |d   �d†|d  |d  | |d   �d‡|d  | |d   �dˆ|d  | |d  |d   �d‰|d  |d  |d  |d   �dŠ| |d  |d  |d   �d‹|d  | |d  |d   �dŒ|d  |d  |d  |d   �d�|d  | |d  |d   �dŽ|d  |d  |d   �d�| | |d  |d   �d�|d  |d   �d‘|d  |d  |d   �d’|d  |d  |d   �d“| |d  |d   �d”|d
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  | | |d   �d°|d  |d  | |d   �d±|d  |d  | |d   �d²|d  | |d  |d   �d³|d  |d  |d  |d   �d´|d  |d  |d   �dµ|d  | |d  |d   �d¶| |d  |d  |d   �d·|d  | |d  |d   �d¸| |d  |d   �d¹|d  |d   �dº|d  |d  |d   �d»|d  |d  |d   �d¼|d  |d   �d½|d  | |d   �d¾|d  |d  | |d   �d¿| |d  | |d   �dÀ|d  |d  |d   �dÁ|d  |d  |d  |d   �dÂ|d  |d  |d   �dÃ|d  |d  |d   �dÄ| |d  |d   �dÅ|d  | |d   �dÆ|d  |d  |d   �dÇ|d  | | |d   �dÈ|d  | |d   �dÉ| | |d  |d   �dy|d  |d   �dÊ| |d  |d   �dË|d  | |d   �dÌ|d  |d   �dÍ| |d   |d d< �dÎ|d  |d  di| |d   �dÏ|d  |d  |  �dÐ|d  |d  |  �dÑ|d  |d  |d   �dÒ|d  |d  |d   �dË|d  |d   �dÓ|d  | |d   �dÔ|d  |d  |d   �dÕ| |d  |d   �dÖ|d  | |d   �d×|d  |d  |d   �dØ|d  | |d   �dÙ|d  |d   �dÚ|d  |d  |  �dÛ|d  |d  |  �dÜ|d
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|d  |d  |  �d|d  |d  |  d7| |d  |d  |  d7|d  |d  |  �d|d  | |d   dŽ|d  |d  |d   �d|d  |d   dÉ|d  | | |d   �d| |d  | |d   dÈ|d  | |d  |d   dÄ| |d  |d   �d|d  |d   �d|d  |d  |d   dH|d  | |d   �d|d  | |d   �d| |d  |d   �d| | |d   �dú|d   |d d< d¤|d  |d  �d|d
  |d
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  |  �d|d  |d  |  �d|�d-  |  �d|�d  |d  |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  |d
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  |d   �d(|d  |d  |d   �d)|d  |d  |d   �d*| |d  |d   �d+|d  |d  |d   �d,|d  |d  |d   �d-|d  |d  |d   �d.|d  |d   �d/| |d  |d
   �d0|�d  |d  |  �d1|d  |d  |  �d2|d  |d  |  �d3|d  |d  |  �d4| |d  |  �d«|�d5  | | |  �d6|d  |d  | |  �d7|d
  |d  | |  �d8|d  |d  | |  �d9|d  |d  | |  �d:|�d-  | |d  |  �d;|d  |d  |d  |  �d<|d  |d  |d  |  �d=|d  |d  |d  |  �d>|d  |d  |  �d?|d  | |d  |  �d@|d  |d  |d  |  �dA|d  |d  |d  |  �dB| |d  |d  |  �dC|d
  | |d  |  �dD|d  |d  |d  |  �dE|d  |d  |d  |  �dF|d  | |d  |  �dG|d  |d  |d  |  �dH|d  |d  |  �dI|d  | |d  |  �dJ| |d  |d  |  �dK|d  | |d  |  �dL|�d  |d   �dM|�d-  |d  |d   �dN|d  |d  |d   �dO|d  |d  |d   �dP|d  |d
  |d   �dQ|d  |d   �dR|�d  | |d   �dS|d  |d  | |d   �dT|d  |d  | |d   �dU|d  |d  | |d   �dV| |d
  | |d   �dW|d  |d  |d   �dX|d
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   |d d< �d“|d  |d  �d|d  |d
   �d”|d  |d   �d•|�d-   �d0|d  |d  |  �d–|d  |d  |  �d—|d  |d
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|d
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iwiH Ïi<Xi~ŠÈ8iËEi@�A i `»iàÐ02iï­i ˜¥i «Ó!iÀŽš i ØLi Xr0i 7i  ªDi ¯/i @KLi¶) i{  iHÎ¬ iLƒãi—¾ iØLI ijsAi(H‘iˆ¯1 i­g�i|oÙiàWi~Ÿ‚iPuri*x'i¬žzvi=
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 i¬ idè i¨ÈW iÐx iÛ iÐŒR inq ih'C i¨qiÂ=i O�i`\¸i8ã	i€Ù
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 iÀ¤	 i Ô0 é€¹* éÀÆ- i¨H  i&Ê  i. i„Þ iò, i¸c iÖó iôi i0–9 i`ƒ�iìŸÌi ?«i !ih< i€© iN iô1 ijöÏiL¹QéìºƒiÔa¹i ÷	i~_@ iDç iJZ iÄäOéàQhi˜Þ	i ‚$iÜ=ixAËi‚ÿFi.Yvi, }Qip  iôÉ  ixi  i²} i6\ i î i 5 é ¡ iœà  é�~  iØA i²  i¨ i �> iŠQ i@KL iâÈ	 iÈ~š ih¶:éæß i˜£'i´ñ5i �´ikñ
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 l   ¯5 iƒ|  iä iDB iJá i…9 i¬'O in° imÍ iÖ6 i”YkizG iÿ iø}i7 éò*iA*Bi”5w id¾:iëmŒl   pIe éX  i6  i¦ž i° r%   iT$  i[’ i)¥ iÜ,Q iRË  iA™ iRoÏ iOciøv6 i?Ý iþA i×q¯i”o€inÑ:é°{ i�¡P i2i²8ßixAi08 iMw�iŠùfi¬†8i7siÐCZ i¸Nèi Rbi‹ai€é*i0&ji�X.i ØŒ6i ;aEi@ôyl    O* i pAvl    PRW iÜP  i3j i{DO i(°!iLV i‹Îd ibž(i¼¸iˆ¤gi/™
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sé æ iy—8iáò&l   1SS l   «Fr iŸ¨Hip+Í iÕ™Žl   :† l   )Mês
 l   9V·* i€‚i@]l   xrì0 l   QDd i g¢ l   �oB  i0!jl   :;A i $u*l   €9	 l   €#Ô4 i  @,l    PAt ì    04< iÂ… iÂ�p iy±igÊiR±­!i50 i�”$i‡eP,l   8bn l   Au´N i\ÃØRé0Y i‹[i'‰ql   ¸L l   “Nä_ l    2 i`_iS)xVl   èä l   Î>;dA l   þmªH, i ¢3l   dj
 l   ê9#pM l    º7: l   %9 i�Y -l   °vV# l   àrÃw l   6V"U l   €&ï l   €
Ö\3 l   Pkêi l    8ì}	 l    T9#< l   @o�g7 l    Ü	 l    p- i�ƒ i—1ièHê l   –PA l   ÄcïS l   .$K inì�l   ‰U) l   ñe l   VL´1 l   gdÊ)* iø‘½ll   G_# l   Ü~ƒ l   BëWÔ l   ­a×  l   Ùt1 l   ,ày¯ l   7g«MÓl   ëKay® l   ðq‘1F l    dñ ?l   «-�l   Ðzš$d l   €8nU1 l   xV­wü l   €QL l    0#¯ l    AWU l    0ao iqýÙi……’Dl   EG<L l   PÔ l   ©R@3 iý&Gl   &®1 l    tÍn[ l   ,d‹!Ò l   ÒTÅIE l   Þ(#A l   &3÷_¯ l   ºì/l   $)l   ë\	A l   ö*ll   õuˆfKl   ,«Tl   (Fëx– l   À,n–l   �Q»MÈl   °RfKš l   °cØs¦l    _íq l   Àa'Çl    hí] iL’¡l   ³3¶g
 l   ­D#3 l   ª)R& l   6#†l   ^ÿNx l   6—-"l   	z–CAl   à~y13l   íXÈy! l   ˆB©*>l   Wjûl}l   °baW4	l   ¨XrÛl   €yÞ'W l   Ž7ä l   é(Íoâ l   § B>l   Ò1/ l   —ILl   k[l   "#ûfzl   &~\àl   ð3�l   €}9
l   `=AKÅ
l   ¶Õl   �o6Šl   Àf½]ql   Î:_l   ‡cGNl   ÁoäŽ l   nJŒJìl   ßub]l   âdUl   HxGUÜl   ‘ŽmTl   GBaâl   ç?” pl   Õ*Æ#¨l   e`ÊTi¨ýÿÿiâ6  i,ª iàH i   iá iÝ¾ i3×E i¾n  iå i×õŒ i´»ÔiU i=3 io’iš;ˆiB±5i i\õiG—i3B†i£‹Æ i6‡û iÊ%?i6ËF&i†)	ihµºi`ÍÑi²9–i`ºmiàE?iX�<#i€†¿pl    OM l    xû iL| i1»' i'F iô{¼ éœÚ i?1 i]— i�›‹iË*/iõÜ‡ iÑãi$�ci(7Ìid�Ÿixt iÈ·	iÿ–:i’Ì}7i.º†i„]Íi2#ÙSl   ª L i,‹|qiðÙq(l   Ø#®N l   Ð/Œk l   ¦d  l   À#8c l   à1� l   `YkD l    Qël l   €pL,- ì    HNZ i&« iDµ$ iBö iÐ9K i0NýiÀâ{ir iÓ¡ iœ?iñ7@ iáÕvri\iàhi�m¶ i
r´iZŸ!l   ðeBv iNÈb	idï±	ipÌpi—Oì,l   ä%ªV l   ’EÜ iÎ8ŸJl   xRU l   :Õi l   ¸ö/8 l   ÈPí- l   @¥5 l   24_QF l    
÷b l   €yb† l   "3<L l   €%à\+ l    XŽp7 l    hˆC! iE£ iÖ‡i‚ï¿#l   šiŸ  iiÿðdi‹j@i<ózsl   ÅJCV
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,\ l   >s=
 l   ÀgÌJ• l   AI@g l   |6D+ l   6*l   ¦3v{ÿ l    y‡#D l   `"€9‡ l   €g l    ¬Q§ i{Tó iÙO l   FI l   *»N# l   ž9«0% iû{¾l   'p� l   Ú~ä_? l   Dï¥ l   $C/y l   Ä3 l   ÐcÆ7úl   rSg)l   ¢H&M l   àJ/à l   $MF?Ô l    RC= l   Ú4®cl   `žW l   (=©S&l    s½O® iý»ûhl   ç`Ðz l   ò]âr7 l   |dzd l   ñ$¼9 l   &O�l   öt~l   ’=2{ l   *7åD¼ l   '_qdl   Ú¢Gl    ï}tl   œMxb l   .vs¼ l   "E$ïl   ­1 %D l   Šž ¤l   ð|cp l   ð/	l   j{®i l   hLÔ/ã l   ü!W0l   b=Al   ? l   ÚX|l   õÏeÿ l   õk8 i~  i:3 iPÊ éÀ  iÌ� i i$ðT iJy  i iZfÁ iZ½³i•Õ+ ij€hi×aX
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é€¨ij†ð iËiŸ¶h7išiœáÌ iJ� l    ¶ i•Ü­Si� l    |§c l   ~m2 l   g*T- i œ�Ll   I3 l   ¨W l    U¢w l    Y|I l    :@ ì    GêP i£2* ii8iÓÍi8øBi¾W i¥Oi/ŽFi„…d-iº°poir€9i'ª?iÃÉhl   �J l   X;=o i˜!­l   úU—d i=$l   ÅVú
 l   ärO l   4ø] l   eto? l   ÐvFe	 l   `3A l   †-' l   À1„b l   €'Çy% l    c” i.= iQv'i/´þl   t4NA i`–Xi©Cl   T¦] l   ŸðX l   txg l   ÔoíL l   ]ï
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l   v�Ÿl   àhî* l   îZçY” l   ¨m»&C l   >C¡Wl l   ™GÿM\l   / Y%‘ l   Œ	ÃKh l   v zEl   )<¹=ql   ÛÚyÆ iH  i°§ i é i® i¿Å  iX*n év/  i¸
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 l   �4”A l   €6>9 iÜ¶†i$$÷)l   bûd l   |—W	 i�ÍÆl   *s÷' l   ^N l   	zf) l   ):UF l   P$` l   š;?yU l   ðq¯$ l   ²uW	 l   :`6# l   2?Fk, l   �
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  |d  |d   dý|d  |d	  |d   dþ|d  |d  |d   dÿ|d  |d  |d   �d |d  |d  |d   �d|d  |d  |d	   �d|d  |d	  |d	   �d|d  |d  |d	   �d|d  |d  |d	   �d|d  |d	   �d|d  |d  |d   �d|d  |d	  |d   �d|d	  |d  |d   �d	| |d  |d   �d
|d  |d  |d   �d|d  |d	  |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  |d	  |d   �d|d  |d   �d|d	  |d  |d   �d| |d	  |d   �d|d  |d  |d   �d|d  |d  |  �d|d  |d  |  �d|d  |d  |  �d|d	  |d  |  �d| |d  |  �d|d
  |d  | |  �d|d  |d  | |  �d|d  |d  | |  �d|d  |d  | |  �d|d  |d  | |  d=|d<  | |d  |  �d|d  |d  |d  |  �d|d  |d  |d  |  �d|d  |d  |d  |  �d |d  |d  |d  |  �d!|d  |d  |  �d"|d  | |d  |  �d#|d  |d  |d  |  �d$|d  |d  |d  |  �d%|d	  |d  |d  |  �d&| |d  |d  |  �d'|d  | |d	  |  �d(|d  |d  |d	  |  �d)|d  |d  |d	  |  �d*|d  |d  |d	  |  �d+|d  | |d  |  �d,|d  |d  |d  |  �d-|d  |d  |d  |  �d.|d  |d  |  �d/|d  | |d  |  �d0|d	  |d  |d  |  �d1| |d  |d  |  �d2|d  | |d  |  �d3|d  |d  |d  |  �d4|d  | |d  |  �d5|d  |d  |  �d6|d<  |d  |d   �d7|d  |d	  |d   �d8|d  |d  |d   �d9|d  |d  |d   �d:|d  |d  |d   �d;|d  |d   �d<|dm  | |d   �d=|d  |d  | |d   �d>|d  |d	  | |d   �d?|d  |d  | |d   �d@|d	  |d  | |d   �dA| |d  | |d   �dB|d
  |d  |d   �dC|d  |d  |d  |d   �dD|d  |d	  |d  |d   �dE|d  |d  |d  |d   �dF|d  |d  |d  |d   �dG|d  |d  |d   �dH|d  |d  |d  |d   �dI|d  |d	  |d  |d   �dJ|d  |d  |d  |d   �dK|d  |d  |d   �dL|d  |d	  |d   �dM|d  |d  |d	  |d   �dN|d	  |d	  |d	  |d   �dO| |d  |d	  |d   �dP|d  |d  |d   �dQ|d  |d  |d  |d   �dR|d  |d	  |d  |d   �dS|d  |d  |d   �dT|d  |d  |d  |d   �dU|d	  |d  |d   �dV|d	  |d  |d   �dW| |d  |d  |d   �dX|d  |d  |d   �dY|d
  | |d   �dZ|d  |d  |d   �d[|d  |d  |d   �d\|d  |d  |d   �d]|d  |d  |d   �d^|d  | | |d   �d_|d  |d  | |d   �d`|d  |d  | |d   �da|d  |d  | |d   �db|d  | |d   �dc|d  | |d  |d   �dd|d  |d  |d  |d   �de|d	  |d  |d  |d   �df| |d  |d  |d   �dg|d  | |d  |d   �dh|d  |d  |d  |d   �di|d  |d  |d  |d   �dj|d  | |d	  |d   �dk|d  |d  |d	  |d   �dl|d  |d	  |d   �dm|d	  | |d  |d   �dn| |d  |d  |d   �do|d  | |d  |d   �dp| |d  |d   �dq|d  |d	   �dr|d  |d  |d	   �ds|d  |d	  |d	   �dt|d	  |d  |d	   �du| |d  |d	   �dv|d  | |d	   �dw|d  |d  | |d	   �dx|d  |d	  | |d	   �dy|d  |d  | |d	   �dz|d  |d  |d	   �d{|d  |d  |d  |d	   �d||d  |d	  |d  |d	   �d}|d  |d  |d	   �d~|d  |d  |d	   �d|d	  |d  |d  |d	   �d€| |d	  |d  |d	   �d�|d  |d	  |d	   �d‚|d  |d  |d	  |d	   �dƒ|d  |d  |d	   �d„|d  |d  |d	   �d…| |d  |d	   �d†|d  | |d   �d‡|d  |d  |d   �dˆ|d  |d  |d   �d‰|d  |d   �dŠ|d  | | |d   �d‹|d	  |d  | |d   �dŒ| |d  | |d   �d�|d  | |d  |d   �dŽ|d  |d  |d  |d   �d�|d  | |d  |d   �d�|d  |d  |d   �d‘| | |d	  |d   �d’|d  |d   �d“|d  |d  |d   �d”|d  |d	  |d   �d•|d  | |d   �d–|d  |d  | |d   �d—|d	  | |d   �d˜|d	  |d  |d   �d™| |d  |d  |d   �dš|d  |d  |d   �d›|d	  |d   �dœ|d	  | |d   �d�| |d  |d   �dž|d  | | |d   �dŸ| |d  |d   �d |d  |d   �d¡|d  |d   �d¢| | |d   |d	< �d£|d  |d  �d¤|d  |d   �d¥|d  |d   �d¦|d
   �d§|d  |d  |  �d¨|d  |d  |  �d©|d	  |d  |  �dª| |d  |  �d«|d  |d	  |d   �d¬|d  |d  |d   �d­|d  |d  |d   �d®|d  |d  |d   �d¯|d  |d  |d   �d°|d  |d	  |d   �d±|d  |d  |d   �d²|d  |d  |d   �d³|d  |d   �d´|d  |d  |d	   �dµ|d  |d	  |d	   �d¶|d	  |d  |d	   �d·| |d  |d	   �d¸|d  |d  |d   �d¹|d  |d	  |d   �dº|d  |d  |d   �d»|d  |d  |d   �d¼|d  |d	  |d   �d½|d  |d   �d¾|d	  |d  |d   �d¿| |d	  |d   �dÀ|d  |d  |d   d÷|d  |d  |  �dÁ|d  |d  |  �dÂ|d  |d  |  �dÃ|d  |d  |  �dÄ|d  |d  | |  �dÅ|d  |d  | |  �dÆ|d  |d  | |  �dÇ|d  |d  | |  �dÈ|d  | |  �dÉ|d  | |d  |  �dÊ|d  |d  |d  |  �dË|d  |d  |d  |  �dÌ|d	  |d  |d  |  �dÍ| |d  |d  |  �dÎ|d  | |d  |  �dÏ|d  |d  |d  |  �dÐ|d  |d  |d  |  �dÑ|d  |d  |d  |  �dÒ|d  | |d	  |  �dÓ|d  |d  |d	  |  �dÔ|d  |d  |d	  |  �dÕ|d  |d	  |  �dÖ|d  | |d  |  �d×|d	  |d  |d  |  �dØ| |d  |d  |  �dÙ|d  | |d  |  �dÚ|d  |d  |d  |  �dÛ|d  | |d  |  �dÜ|d  |d  |  �dÝ|d  |d  |d   �dÞ|d  |d	  |d   �dß|d  |d  |d   �dà|d	  |d  |d   �dá| |d  |d   �dâ|d
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  |d   �d^|d  |d  |d   �d_|d  |d	  |d   �d`|d  |d  |d   �da|d  |d  |d   �db|d  | |d   �dc|d  |d  | |d   �dd|d  |d	  | |d   �de|d  |d  | |d   �df|d  | |d   �dg|d  |d  |d   �dh|d  |d  |d  |d   �di|d	  |d	  |d  |d   �dj| |d  |d  |d   �dk|d  |d  |d   �dl|d  |d  |d  |d   �dm|d  |d	  |d  |d   �dn|d  |d	  |d   �do|d  |d  |d	  |d   �dp|d	  |d	  |d   �dq|d	  |d  |d   �dr| |d  |d  |d   �ds|d  |d  |d   �dt|d  | |d   �du|d  |d  |d   �dv|d	  |d  |d   �dw| |d  |d   �dx|d  | | |d   �dy|d  |d  | |d   �dz|d  |d  | |d   �d{|d  | |d  |d   �d||d  |d  |d  |d   �d}|d  |d  |d   �d~|d	  | |d  |d   �d| |d  |d  |d   �d€|d  | |d	  |d   �d�| |d  |d   �d‚|d  |d	   �dƒ|d  |d  |d	   �d„|d  |d	  |d	   �d…|d  |d	   �d†|d  | |d	   �d‡|d	  |d  | |d	   �dˆ| |d	  | |d	   �d‰|d  |d  |d	   �dŠ|d  |d  |d  |d	   �d‹|d  |d  |d	   �dŒ|d  |d  |d	   �d�| |d	  |d	   �dŽ|d  | |d   �d�|d  |d  |d   �d�|d  | | |d   �d‘|d  | |d   �d’| | |d  |d   �d“|d	  |d   �d”| |d  |d   �d•|d  | |d   �d–|d  |d   �d—| |d   |d< �d£|d  |d  �d˜|d  |d   dñ|d  |d   �d™|d  |d	  |  �dš|d  |d  |  �d›|d  |d  |  �dœ|d  |  �d�|d  |d  |d   �dž|d  |d	  |d   �dŸ|d	  |d  |d   �d | |d  |d   �d¡|d  |d  |d   �d¢|d  |d	  |d   �d£|d  |d  |d   �d¤|d  |d  |d	   �d¥|d  |d	  |d	   �d¦|d  |d	   �d§|d	  |d  |d   �d¨| |d	  |d   �d©|d  |d  |d   d÷|d  |d  |  �dª|d  |d  |  �d«|d	  |d  |  �d¬| |d  |  �d­|d  | | |  �d®|d  |d  | |  �d¯|d  |d  | |  �d°|d  |d  | |  �d±|d  | |d  |  �d²|d  |d  |d  |  �d³|d  |d  |d  |  �d´|d  |d  |  �dµ|d  | |d  |  �d;|d	  |d  |d  |  �d¶| |d  |d  |  �d·|d  | |d	  |  �d¸|d  |d  |d	  |  �d¹|d  | |d  |  �dº|d  |d  |  �dÝ|d  |d   �d»|d  |d  |d   �d¼|d  |d	  |d   �d½|d  |d  |d   �d¾|d  |d   �d¿|d  | |d   �dÀ|d  |d  | |d   �dÁ|d	  |d	  | |d   �dÂ| |d  | |d   �dÃ|d  |d  |d   �dÄ|d  |d  |d  |d   �dÅ|d  |d	  |d  |d   �dÆ|d  |d  |d   �dÇ|d  |d  |d  |d   �dÈ|d	  |d  |d   �dÉ|d	  |d	  |d   �dÊ| |d  |d	  |d   �dË|d  |d  |d   �dÌ|d  |d  |d   �dÍ|d  |d  |d   �dÎ|d  | | |d   �dÏ|d  |d  | |d   �dÐ|d  | |d   �dÑ|d	  | |d  |d   �dÒ| |d  |d  |d   �dÓ|d  | |d  |d   �dÔ| |d	  |d   �dÕ|d  |d	   �dÖ|d	  |d  |d	   �d×| |d	  |d	   �dØ|d  | |d	   �dÙ|d  |d  | |d	   �dÚ|d  |d  |d	   �dÛ|d  |d  |d	   �dÜ| |d  |d	   �dÝ|d  | |d   �dÞ|d  |d   �dß| | | |d   �dà|d  |d   �dá| |d   |�dâ< �dã|d  |d  �dä|d  |d   �d¦|d   �då|d  |d	  |  �dæ|d	  |d  |  �dç| |d  |  �dè|d  |d  |d   �dé|d  |d	  |d   �dê|d  |d  |d   �dë|d  |d  |d   �dì|d  |d	  |d   �dí|d  |d   �dî|d	  |d  |d	   �dï| |d	  |d	   �dð|d  |d  |d   �dñ|d  |d  |  �dò|d  |d  |  �dó|d  |d  |  �dô|d  | | |  �dõ|d  |d  | |  �dö|d  |d  | |  �d÷|d  | |  �dø|d  | |d  |  �dù|d	  |d  |d  |  �dú| |d  |d  |  �dû|d  | |d  |  �dü|d  |d  |d  |  �dý|d  | |d	  |  �dþ|d  |d	  |  �dÿ|d  |d   �d |d  |d  |d   �d|d	  |d	  |d   �d| |d  |d   �d|d  | |d   �d|d  |d  | |d   �d|d  |d	  | |d   �d|d  |d  |d   �d|d  |d  |d  |d   �d|d	  |d  |d   �d	|d	  |d  |d   �d
| |d  |d  |d   �d|d  |d	  |d   �d|d  | |d   �d|d  |d  |d   �d|d  |d   �d|d	  | | |d   �d| |d  | |d   �d|d  | |d  |d   �d| |d  |d   �d|d  |d	   �d|d  |d  |d	   �d|d  | |d	   �d|d  | |d	   �d| |d  |d	   �d| | |d   �d|d   |d< |S (  Nr   r   rM  rS   i0\  r/   r(   rµ   r   rU  ià`  rJ   r   i€e iR< r   i�­ r   i0 i¬•, r?   i`çiÆï�r!   i¸å�i¨ø r   iz~˜ iï>i¢¢Ui¸ré€ô iÜ¤iþ$(is—Nl   ó9 i`ÏÀ i˜O.l   <Ç l   ìrý iÿž“i€…œl   àW l   l^ iø¿3_i@•tl   €`o l   `nP' l    _— l    2D7 l     Šw l    G$	 l    p÷ r^  i ×  i v
 iš° iP~>i˜r£rE   r]  i�{Š iÎy ižŸ5i\áji(C ir@xi¬YÍl   €^P( l   -nT
 i » i�Ñi0Ë«!l   °m› l   Ri! icg/iðGi�¨t\iÌƒ´il   %tÓ10 l   ¹3ðw iÀBhIl   @A¢ l   €§$ l   ÐrR l   €M¸	 l   @h|6 l   ÀSö† l    TãD) l    rj! l    ¨u: l     h18 l     ~ l    ƒ?" l    `ìO8 l    `Z, i°d	 iT—  iR9iêÀGiLæ‹Ai8+3 i¦Bmi6:zl   @*)8 l   f,X= ipYzRi€˜# r%   i4žéiî¼°5l   T{bW l   87 l   ŽbHC% i€Ã¥l   ¤Pºx l   àMö` l   ~iý6* l   (Nkl   À1J l   PQ›B" l   ;²IT l   €+ÀcHl   ³Lr¨ l   @8)i l   À<ëdè l   T¬gël    	,K l   @V�x² l    rŠKdl    WD;nl    SÓel    8Âl    ry)l    l�x:l    p™bl    PÍ'iø^! i~�ÓiþÄ
l   P,ü	 l   çfÎP l   TOj i´Yxi®_Ý2l   ¶P@ l   „@š,¥ l   ]ØAi`¼%	l   H;´ l   ³(ï5@l   xpö,ñl   —Ã)=l   0~”7 l   Tç,l   ?LcÌl   øD`GM l   @1˜e˜ l   0IË>l    M«x;l   À?@Lœl   €~`Íl   `	+

l     ´¹l    ^04·l    ,Hl|l    `%K]ihi
€5Ol   ‘=ñ l   ,j� l   Ðjör€l   H%d:Ð iØ�]*l   É›* l   ØÅ`$l   ¦S¹El   `$­l   ²t l   é‡Q0 l    FIhl   -M£J8l   ¸A}%@l   ODÿl   *g %<l   â©pÁl   `% lYl   ´3(\à5l   0íK�l   €ÊyBl    1'd|l    ~öF$+l    TÑiN&l    `¼wÓl   J=iU
 l   ¨t=‹ l   -	ül   pFël   âþgYl   íb™]—l   ŠkXrÐl   …Zû#El   (bËl   cisâl   
ë0™l   �aÜ|È&l   08sHg l   À ‡Wl   `n…<#xl    Rœ$ã l   ²=´tW l   î�hýl   wY>K
l   Š]ð
�l   _=ÌD l   "ní2l   sh¯0µO l   ùg=r÷l   4X
 l   ²<*.Àxl   LL¨O×7 l   €D@é9 l   `.”P5 l    BRÕ$l   š¢Uâ	l   ä`pL)l   Ñk2lo	l   I2UŒ+ l   PcppkH l    hÂ;i l    6ÑXal   Ãø&àl   l'M&+X l   TT‘H  l   �=€.ö9 l   xkSl	 l   õ.Ü¹F r-   i@Q  i,°  i N rD  iPy iè i³3( iØJ( iP' iU i_ i&O· iî�»r\  i\6 iÄÁ›i¥žò i\¾‹iÐî1 i‚²‹i;P0ib%ji—?êixU·iƒ%ioƒl   úlÚ# i€ÐRi<3l   8|, i ©b&l   €}x l   À}) i èel    E0e ra  rE  i`º i˜é  i!àpilri ñ igT id¤8 i{÷viËì}Bixçi<Ô¤i¹9l   B;¦	 iÀD:9i0eiil'Gihªl   Ñ<âT	 l   v
7* iÐ­—l   ÀX[ l   D0ì? l   ÞIr
 l    a
i l   07� l   oÒO, l   (3À l    FU l   €*l( l   Àb( l     f l    Måj9 l    0×( l    PC is il=) išeNiU i´$&`ihYr_  it+Ø i$K…l   4[´7 l   !Glh
 l   ¢b×D ipÞŸiNÀiÓ5txl   J@ür l   pji~ ixI¨;l   ð¥# l   Õ	g l   @&{f)l   >d‘}/ l   xv´` l   Ð/+/Z l   ¾RíSµl   ì{±*l   €¡aY l   €y,l   8n=l    QòjŸl    #$
l   ÀÕßl     q0l    p’e.l    8´;•iP4ziL=^'l   +µ= l   ¬r l   ;Xjb iU1l   äy�6 l   2d% l   üJ�Rg l   0!q0 l   ¤;eE l   ðRG~ l   M	=_¤ l   ú¡$fl   Ð_‘pŸ l   ÈÃG<l   jmX�l   �UÍ@¶l    [°AËl   Hq–XÂ
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  i”Ù  iPŒ i€Ý i@j  i(¯
 iVaW i�ãå iÌ# i7¢+ i-´Ûi‚è%rF  ià8A i!¬ˆiÆùÊi@0âit! iDd„i»¢/iecÒFiŒ$uiÐ¼}6l   .£ iÐ÷Ål    *)V l   ts› i@8Mll    ! rd  i|Ñ iÆÝ i–ãGiØ išÅ® iHci9WSiN¾i8µ i/ZÐ i�‘Ã	iÏV
l   ƒ0©f i„Æ iz)iÁRl   
j¿ ix@QiLfJi0ÞYl   ŸäZ i ‹ôCi ˆl   P W l   €*Àc l   @[®! i NrSl    F))$ i\É i·wI i%)0iR–<l   àü rI  i
�Îi9ç÷Al   u#k
 l   $ãI iäŠCi%ºl   HLD l   }›~X l   ´B|E
 i|þïgl   dkÚ  l   ¯
R¥ l   ;bwp l   „>ª l   `N×è l   Åj¡®l   p>N¥ l   @Ä,¤l   tÖ7xl   ÀBŽl    ÉA{l    	WP{ih†i©´ëLl   C l   ¢KDB l   @Â& i$Ôh5l   ðr¸4 l   Z= M l   gCl   úBm l   lq*l   øFÊl   T=5 Il   $2Zl   7É2Žl    eâ(l   pKHMÂl   @N“ôl    VŒiï‘�l   o l   ÞiéW\ l   Î?Âk l   ïZ}@ l   •r(7] l   �'$a·l   Kå Wl   PAMŸ l   è0�vl   ß#hl   �ÿ l   ‰Á$l   ÀÑH�l   Œq>°l    SzG‚l   À4¸-~ l   QXòT£l   ƒA18 l   ‰89±l   �
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†ul   c{­ ‘l   ¾?ÙB0"l   tqŸXl   êcÝl   A8Xav l   Ñß)¬l   ŒQáâ-l   	$ÍWÑ\l   KD« l   –4Ñ&Eið#  i0ì é@8  iÒ i\ ihž� rS  iž` iíTE iýÍëi $qiÒt iÀª… iA/2iìoiJ@ iéÛX
iu	ì&rW  iÈÅô1iÄ)|"i`”i�™krg  i„Q iaMQ iJ”iH Ãi`÷ iT iì5ùióš¨
i0åFiPüg i9/id¸diY½iä_icc÷Aižè'l   ÙV i0*Ý;l   Øvr l   ¨e# l   À:Ÿ i0žõi ñSel    I²c	 iæû• iÃÑÍi¬i
»*iž5iUái?½�ziuÇO-l   Pn i¬æŠl   Et: l   ¤Fà( l   13k l   –– l   ¨
…G( l   }ƒ0L l   È&F( l   P”d• l   4 "\ l    ^	„ l    77m l   €}´« in$7	l   N|„
 l   ÑAŸ3 l   S,  l   X1¹G l   âaÍi? l   "yõr„ l   ‘B.2E l   ük6jl   AP*ü l   øC¬AUl   PvpGtl   �%tU¬l    !p<ô iPÓ l   Àòl l   (î§ l   .=Þ l   É6Y9 l   ôJÇ<ú l   šëYal   �\£P‚ l   yAøhl   Øumïl   œJ?~àl   �X ,Dl   ü vu l   kú/l   öfœl   ç/JwÌl   ˜	<l   ƒNlk• l   “F�l   ‡<k”l   ,x571l   ÏRIiT¡  ipb  iˆG ióØ3 iØÀW i|Ý  i� iú.i¶Ïþiˆô iaçñiN:ViD#iˆ¶Ž
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|d  |d
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  |d   �d|d  |d  |d   �d|d  |d  |d   �d| |d  |d   �d|d  | |d   �d|d  |d  |d   �d|d  |d  |d   �d|d  | |d   �d|d  |d  |d   �d|d  |d   �d|d  | |d   �d| |d  |d   �d|d  | |d   �d|d  |d  |  �d|d  |d  |  �d|d  |  �d|d  |d  | |  �d|d  |d  | |  �d| |d  | |  �d |d  |d  |d  |  �d!|d  |d  |d  |  �d"|d  |d  |d  |  �d#|d
  |d  |  �d$|d  |d  |d  |  �d%|d  |d  |d  |  �d&|d  |d  |  �d'|d  |d  |  �d(|d  |d  |d  |  �d)| |d  |d  |  �d*|d  |d  |  �d+|d  |d  |d  |  �d,|d  |d  |  �d-|d  |d  |  dÐ|d  |d  |d   �d.|d  |d  |d   �d/|d  |d  |d   �d0|d
  | | |d   �d1|d  |d  | |d   �d2|d  |d  | |d   �d3|d  | |d   �d4|d  | |d  |d   �d5|d  |d  |d  |d   �d6| |d  |d  |d   �d7|d  | |d  |d   �d8|d  |d  |d  |d   �d9|d  | |d  |d   �d:|d  |d  |d   �d;| | |d  |d   �d<|d  |d   �d=|d  |d  |d   �d>|d  |d  |d   �d?| |d  |d   �d@|d  | |d   �dA|d  |d  | |d   �dB|d  |d  | |d   �dC|d  |d  |d   �dD|d  |d  |d  |d   �dE|d  |d  |d   �dF|d  |d  |d   �dG| |d  |d  |d   �dH|d  |d  |d   �dI|d  |d   dû|d  | |d   �dJ|d  |d  |d   �dK|d  |d   �dL|d  | | |d   �dM| |d  | |d   �dN|d  | |d  |d   �dO| |d  |d   �dP|d  |d   �dQ|d  |d  |d   �dR|d  | |d   �dS|d  | |d   �dT| |d  |d   �dU| | |d   �dV|d   |d< �dW|d  |d  �dX|d  |d
   �dY|d  |d  |  �dZ|d  |d  |  �d[|d
  |  �d\|d  |d  |d   �d]|d  |d  |d   �d^| |d  |d   �d_|d  | |d   �d`|d  |d  |d   �da|d  |d  |d   �db|d  | |d   �dc|d  |d  |d   �dd|d  |d   �de|d  | |d   �df| |d  |d   �dg|d  | |d   �dh|d  |d  |  �di|d  |d  |  �dj| |d  |  �dk|d  |d  | |  �dl|d  |d  | |  �dm|d  |d  | |  �dn|d
  |d  |  �do|d  |d  |d  |  �dp|d  |d  |d  |  �dq|d  |d  |  �dr|d  |d  |  �ds|d  |d  |d  |  �dt| |d  |d  |  �du|d  |d  |  �dv|d  |d  |d  |  �dw|d  |d  |  �dx|d  |d  |  �dy|d
  | |d   �dz|d  |d  |d   �d{|d  |d  |d   �d||d  |d   �d}|d  | | |d   �d~|d  |d  | |d   �d| |d  | |d   �d€|d  | |d  |d   �d�|d  |d  |d  |d   �d‚|d  | |d  |d   �dƒ|d  |d  |d   �d„| | |d  |d   �d…|d  |d   �d†|d  |d  |d   �d‡|d  |d  |d   �dˆ|d  | |d   �d‰|d  |d  | |d   �dŠ|d  | |d   �d‹|d  |d  |d   �dŒ| |d  |d  |d   �d�|d  |d  |d   �dŽ|d  |d   �d�|d  | |d   �d�| |d  |d   �d‘|d  | | |d   �d’| |d  |d   �d“|d  |d   �d”|d  |d   �d•| | |d   |d< �d–|d  |d  dœ|d
   dœ|d  |d  |  �d—| |d  |  �d˜|d  |d  |d   �d™|d  |d  |d   �d|d  | |d   �dš|d  |d  |d   �d›|d  |d   �dœ|d  | |d   �d�| |d  |d   �dž|d  | |d   �dŸ|d  |d  |  d |d  |d  |  d|d  |d  | |  �d |d  |d  | |  �d¡|d  | |  �d¢|d  |d  |  �d£|d  |d  |d  |  �d¤| |d  |d  |  �d¥|d  |d  |  �d¦|d  |d  |d  |  �d§|d  |d  |  �d¨|d  |d  |  �d©|d  | |d   �dª|d  |d  |d   �d«| |d  |d   �d¬|d  | | |d   �d­|d  |d  | |d   �d®|d  | |d  |d   �d¯|d  |d  |d   �d°| | |d  |d   �d±|d  |d   �d²|d  |d  |d   �d³|d  |d   �d´|d  | |d   �dµ| |d  | |d   �d¶|d  |d  |d   �d·|d  |d   �d¸|d  | |d   �d¹| | |d   d‡| |d   |�dº< �d|d  |d  d| |d   �d	|d  |d  |  �d
|d  |d  |  dœ|d  | |d   �d»|d  |d  |d   �d¼|d  |d   �d½|d  | |d   �d¾| |d  |d   �d§|d  | |d   dœ|d  |d  |  �d¿|d  |d  |  �dÀ|d  |  �dÁ|d  | |  �dÂ|d  |d  | |  �dÃ| |d  | |  �d}|d  |d  |  �dÄ|d  |d  |d  |  �d§|d  |d  |  �dÅ|d  |d  |  �dÆ|d  | |d   �dÇ|d  |d  |d   �dÈ|d  | | |d   �dÉ|d  | |d   �dÊ| | |d  |d   �d²|d  |d   �dË| |d  |d   �dÌ|d  | |d   �dÍ|d  |d   �dÎ| |d   |d< |S (Ï  Nr   r   iØÿÿÿr   rJ   i  r   r   i¼  r?   i-  r!   i  i†  r/   ie|  r   i�Q  i­%  r   iá  iow iX  id½ i´ içh  rr  rS   i€- i€¥M i˜  i  i uX i@‰ i Ø' i Hq i s# i @ƒ i ˆ� i @œ iô  i­˜  iÌ r(   iäŽ  iùï iÄ i­2 i5% iƒð¤ iÂê iøÈ iª.E i"»�iuOE rC  iP±! iø;ziÌ¥ i ž i€h: i`l’ ipËYi Ä; i Éi€ii àÄ i  0i `ê rö   i¶”  i¬¥ i'H' i$Ï iÏw ihäN i-ÿ©i¼§Oi(À iÎCÞ iwè?iî°¿i˜Ý§ iH:Ïi.‹t	i¤”©i€‹¾i £i8�íi ÓŒ	i€@ói À'	i 'i HèiWò iŽÉ  iRÐ rZ  ih� i÷é´ imi§�@id CiÐ~° i,êëi<}Á%iÒipLki@ôÌ!icM)i€!xiÀº4iÐNi ì`!i wGi 8œi ÐiÉó i’¤iV0i´K˜iIÜ—i·V„'i)‚€iÌ~I iFÖ=KijËÌi@Ðº%iØÔ\Ki@É«@l    ;ÝA iÆ×i]VŠiÎ0i^Ð² i’IÌ*iÖ!Übl   Ì l   (ajT l   <{n} l   `Aé l   P&f= i€áNhii­Pi Û!]l   æ6¥X l   Äy] rX  iÆhl   FYz l   ô)W  rB  r¢   rD   én   i8  i0  iô  iÚC  i"  i)  iÆÄ iÊ  iòb  iäØ iæô ià  i@B  i0s i… i   i`ž i@¿U i H i m¡ i€ß, i �~ i Ï iH  iœ  id_  i¤  i”o i¨7 i89 i˜X  ib¶ iT, iÚÚT i 2  i¼i ip—f i¸„gi€æ iàòY iÐeiìøUi ò i@°ÁiÀÜ/i 9 i ,"i ø$iz  ipÊ i2Œ
 i^ rG  i
 iœp iÎô i¢0 iØV iÄ²L it�i€Ûý rH  iÊ6Qi ®i@ÎŒ
i %‹i _L	iÜª  i.Â i„Cƒ iê!î i(¡\iØx iõši€*i V	i,ò…ip¦÷ rP  i`Åß	i`(Ci9Øi@V·i€¦í"i 4I#iž, i²&ºi:Ót iÂ‰i‚Íð iRi�çpDi*r~i€ýœvl   €/‚w i²Ÿ& ie'i¦dÜOiðûiL5ƒ(i^_ l   tw‰b r›   i6/_;l   @7‡t l   úT+  rY  rn  éP   r[  i¢  iÎ  i¤Q  i’¸  iÆ  iÖK iæ iÐ  iØL i4Ž iÀ i �8 ið¸ i §+ i€ªk i ô~ i 
  iµ  i¸ iŒd  ix iž×  ixð  i–í i”@Š ia  iÜÒ iJ(iæ>� i`Ö iPŸ iÈ£ði€� i@aÝi â i ±ž i>ú iÚæ  iä iÔð+ i w¿ iÈiÜ iâU1 iˆ¥²iR)NiH³éixû¦rQ  i Ð­i€±Orf  iŠ iœÒ, iš¶‹ iÜ' i€¯ü iÎ�iÜˆóid°
iÞGAi�8�	ipi@	åi Irl  i¦÷_iFàiêG.id#/i°w•Qià÷i*SOi^s”išRgjix¦˜ rL  i¢”éx   i*  i   iÈ#  iÄ  i²  i �  iÖ°  rR   iøí  ir iày  i`C iXÅ i€õ i€� i ." i   iÎ;  iè  iÜ#  i(Â iRÿ rh   i&Õ i&à& iÐ;! rq  ixé> i ‡² i€N i Tù i Ä	 rN  i~	  i²Ô  i<[ iŒ:* rE  iû iDüÜ ipUI iT›É iÀ’ƒr  rv   r`  iþi iú�e iZ{f iHpi¸Mli	’iðºià$7i€,iü¦iîxoiò@‚	iØ7ór  i¨ÕiPÖÜr,   i"  iæ  iÄO  i Z  i8 i€‰  i * i S iÀ  iø  ià iˆ  i<Þ iª� i@d i@¬' i€8 iÀ'	 r-  iÀÔ iV- i"} iz# rÏ   ixÞ+ i`ã rK  rT  iÔe rs  iô!Ë i @Ý iÀáä ip89 iÜ\$r   iÀ+  re  rb  i ú  iÂ3  rJ  i¨  iºÛ  rÇ   i€‹ i † rd   éèn i » iD• rR  r  rO  i %& iNrS ro  )r   r   r   r   r   Úcr   r   r   rz  ƒ   sr    
ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ oÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ,ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ 3ÿ ÿ ÿ ÿ ÿ ÿ äÿ ÿ ÿ ÿ dÿ ÿ üzPolyQuintic.cc                 C   s¼  | j | j| j| jf\}}}}d|d  |d  d|d  |d   d|d   d|d	  |d  |  d
|d  |d  |  d| |d  |  d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  |d  |d   d|d  |d  |  d|d  |d  |  d|d  |d	  |  d|d  | | |  d|d  |d  | |  d|d  |d  | |  d|d	  | |  d|d	  | |d  |  d|d  |d  |d  |  d| |d  |d  |  d |d  | |d  |  d!|d  |d  |d  |  d"|d  |d   d#|d	  |d  |d   d |d  |d  |d   d$| |d  |d   d%|d  | |d   d&|d  |d  | |d   d'|d  |d  | |d   d(|d  |d  |d   d)|d  |d  |d  |d   d*|d  |d  |d   d+|d  |d  |d   d,|d  |d  |d   d-|d  |d   d.|d  | | |d   d/| |d  | |d   d0|d  | |d  |d   d1|d  |d   d2|d  |d  |d   d3|d  | |d   d4|d  | |d   d5|d   }|S )6Nr   r   é;   r!   r   éØ   rS   é$   r/   io  i2
  éQ   r   iß  r   iI*  rh  i\D  r>   i'  r<   i0  iD  iæ  r?   iø%  iú¯  r7  r¤   iTi iô~  i`ê  r:  iÙ  re  r4  i1G  iŒ­ i­K iX iPø i	=  i�Ð ry  i˜« ri  i¬ iÐ i}) r  iTê* iáõ rV  ro  )r   r   r   r   r   ÚFr   r   r   r  –   s    ÿ ÿ ÿ ÿ  zPolyQuintic.Fc                 C   s$   | j }| j}t|tƒ |¡| }|S ©N)r  ru  r   r	   Úeval)r   Úthetar  ru  Úl0r   r   r   rƒ  œ   s    zPolyQuintic.l0c                 C   s¤   | j }dgd }| j}t|d tƒ |¡ d|  |d< t|d tƒ |¡d| |  |d< t|d tƒ |¡d|  |d< t|d tƒ |¡d| |  |d< |S )Nr   r   r   r   r!   r   )r  rp  r   r	   r�  )r   r‚  Údr  ÚTrp  r   r   r   r…  ¢   s    
"$ $zPolyQuintic.Tc                 C   s,   | j }| j}t|tƒ |¡||  }t|ƒS r€  )r  rt  r   r	   r�  r   )r   r‚  r„  r  rt  Úorderr   r   r   r†  ­   s    zPolyQuintic.orderc                 C   sD   | j }| jtddƒ }t|tƒ |¡d| | j  }t|ƒt|ƒfS )Niçÿÿÿr   )rz  r   r   r   r	   r�  r  r   )r   r‚  r„  rz  ÚuÚvr   r   r   Úuv³   s    zPolyQuintic.uvc                 C   s   | j | j| j| jgS r€  )r   r   r   r   )r   r   r   r   Úzeta¹   s    zPolyQuintic.zetaN)Ú__name__Ú
__module__Ú__qualname__Ú__doc__r   ÚpropertyrF   rp  rt  ru  rz  r  rƒ  r…  r†  r‰  rŠ  r   r   r   r   r
      s(   

6



r
   N)rŽ  Z
sympy.corer   Zsympy.core.evalfr   Zsympy.core.numbersr   r   Zsympy.functionsr   Zsympy.polys.polytoolsr   Zsympy.utilitiesr   r	   r
   r   r   r   r   Ú<module>   s   