o
    oh#w                    @   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ZeG d	d
 d
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

    )Symbol)N)IRational)sqrt)Poly)publicxc                   @   s   e Zd ZdZdd Zedd Zedd Zedd	 Zed
d Z	edd Z
edd Zdd Zdd Zdd Zdd Zedd ZdS )PolyQuinticz'Special functions for solvable quinticsc                 C   s   |  \}}| _| _| _| _tddtdd  tttdd tdd   | _td d tdd tttd d tdd   | _	td d tdd tttd d tdd   | _
tddtdd  tttdd tdd   | _d S )N            )
all_coeffspqrsr   r   r   zeta1zeta2zeta3zeta4)selfpoly_ r   p/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/polys/polyquinticconst.py__init__   s
   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
|d  |d   d|d  |d   d| |d  |d   d|d  |d   d|d   d|d  |d  |  d|d  |d  |  d|d  | | |  d|d  |d  | |  d|d  | |  d|d  | |d  |  d| |d  |d  |  d|d  | |d  |  d| |d  |  d|d  |d   d|d  |d  |d   d| |d  |d   d|d  | |d   d|d  |d  | |d   d|d  |d  |d   d|d  |d  |d   d| |d  |d   d| | | |d   d |d  |d   d!| |d   d| |d  d"|d  |d  |  d#|d  |d  |d   d|d  |d   d$|d  |d   d%| |d  |d   d|d  |d   d&|d   d'|d  |d  |  d(|d  |  d)|d  | | |  d*| |d  | |  d+|d  | |d  |  d,| |d  |  d-|d  |d   d.|d  |d  |d   d/|d  | |d   d0|d  | |d   d1| |d  |d   d2| | |d   d |d   t  |d |d  d|d  |d  |  d|d  |  d3|d  |d   d%| |d  |d   d4|d  |d   d5|d   d6| |d  |  d7|d  | | |  d8| |d  |  d2|d  |d   d1| | |d   td   d|d  d9| |d  |  d:|d  |d   d|d   d;|d  | |  d5| | |  d| |d   td   d| |d  d|d  |  d:|d   d6| |  td   d| td   td  }t|tS )<Nr         r      A   r            0                  |      iN     @           }   c   i  i  i  i    i5  i$     3       L   i      :   u   i   i  i`	  l   iE  i  i
    q  	      i  2   Z   ix     (      )r   r   r   r   r	   r   )r   r   r   r   r   f20r   r   r   rH       s        h 
zPolyQuintic.f20c                 C   s  | j | j| j| jf\}}}}g g dg dg dg d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$|d  |d  |  d%|d  |d
  |  d&|d  |  d'|d  |d  | |  d(|d  |d  | |  d)|d  |d  | |  d*| |d
  | |  d+|d  |d  |  d,|d
  |d  |d  |  d-|d  |d  |d  |  d.|d  |d  |d  |  d/|d  |d  |  d0|d  |d  |d  |  d1|d  |d  |d  |  d2|d  |d  |  d3|d  |d  |  d4|d  |d  |d  |  d5| |d  |d  |  d6|d  |d  |  d7|d  |d  |d  |  d8|d  |d  |  d9|d  |d  |  d:|d  | |d   d;|d
  |d  |d   d<|d  |d  |d   d=|d  |d  |d   d>|d  | | |d   d?|d  |d  | |d   d@|d  |d  | |d   dA|d  | |d   dB|d  | |d  |d   dC|d  |d  |d  |d   dD| |d  |d  |d   dE|d  | |d  |d   dF|d  |d  |d  |d   dG|d  | |d  |d   dH|d  |d  |d   dI| | |d  |d   dJ|d  |d   dK|d  |d  |d   dL|d  |d  |d   dM| |d  |d   dN|d
  | |d   dO|d  |d  | |d   dP|d  |d  | |d   dQ|d  |d  |d   dR|d  |d  |d  |d   dS|d  |d  |d   dT|d  |d  |d   dU| |d  |d  |d   dV|d  |d  |d   dW|d  |d   dX|d  | |d   dY|d  |d  |d   dZ|d  |d   d[|d  | | |d   d\| |d  | |d   d]|d  | |d  |d   d^| |d  |d   d_|d  |d   d`|d  |d  |d   da|d  | |d   db|d  | |d   dc| |d  |d   dd| | |d   de|d   |df d< dg|d  |d  dh|d  |d   di|d  |d  |  dj|d  |d  |  dk|d  |  d$|d  |d  |d   dl|d  |d  |d   dm| |d  |d   dn|d
  | |d   do|d  |d  |d   dp|d  |d  |d   dq|d  | |d   dr|d  |d  |d   ds|d  |d   dt|d  | |d   du| |d  |d   dv|d  | |d   dw|d  |d  |  dx|d  |d  |  dy| |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  |  d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | | |d   d|d  |d  | |d   d| |d  | |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d  | |d  |d   dH|d  |d  |d   d| | |d  |d   d|d
  |d   d|d  |d  |d   d|d  |d  |d   d|d  | |d   d|d  |d  | |d   d|d  | |d   d|d  |d  |d   d| |d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  |d   d|d  | | |d   d| |d  |d   d|d  |d   d|d  |d   d| | |d   |df d< d|d  |d  d|d  |d   d|d   d|d  |d  |  d|d  |d  |  d| |d  |  d'|d
  | |d   d|d  |d  |d   d|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  |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
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  |d
  |  d,|d  |d  |  d-|d  |d.  |  d/|d  |d  | |  d0|d  |d
  | |  d1|d  |d  | |  d2|d.  | |  d3|d  |d  |d  |  d4|d  |d  |d  |  d5|d  |d
  |d  |  d6| |d  |d  |  d7|d  |d  |d  |  d8|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  |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  |d   dM|d  |d  |d   dN|d  |d  |d   dO| |d  |d   dP|d  |d  | |d   dQ|d
  |d  | |d   dR|d  |d  | |d   dS|d  |d  | |d   dT|d.  | |d  |d   dU|d  |d  |d  |d   dV|d  |d  |d  |d   dW|d  |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   da|d  |d  |d  |d   db|d  |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   di|d  |d  |d   dj|d  |d
  |d   dk|d  |d   dl|d  | |d   dm|d  |d  | |d   dn|d  |d  | |d   do|d  |d  | |d   dp| |d
  | |d   dq|d  |d  |d   dr|d
  |d  |d  |d   ds|d  |d  |d  |d   dt|d  |d  |d  |d   du|d  |d  |d   dv|d  |d  |d  |d   dw|d  |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
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|d  |d  |d  |  d|d  |d  |  d|d  |d  |  d7| |d  |d  |  d7|d  |d  |  d|d  | |d   d|d  |d  |d   d|d  |d   d|d  | | |d   d| |d  | |d   d|d  | |d  |d   d| |d  |d   d|d  |d   d|d  |d  |d   dH|d  | |d   d|d  | |d   d| |d  |d   d| | |d   d|d   |d d
< d|d  |d  d|d
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   d1|d  |d  |  d2|d  |d  |  d3|d  |d  |  d4|d  |d  |  d5| |d  |  d|d6  | | |  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  |  dA|d  |d  |d  |  dB|d  |d  |d  |  dC| |d  |d  |  dD|d
  | |d  |  dE|d  |d  |d  |  dF|d  |d  |d  |  dG|d  | |d  |  dH|d  |d  |d  |  dI|d  |d  |  dJ|d  | |d  |  dK| |d  |d  |  dL|d  | |d  |  dM|d  |d   dN|d.  |d  |d   dO|d  |d  |d   dP|d  |d  |d   dQ|d  |d
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|d
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< d|d  |d  d|d  |d.   d|d  |d6   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  |d  |  d| |d  |d  |  d|d  | |d  |  d|d  |d  |d  |  dQ|d  | |d  |  d|d  |d  |  d|d6  |d   d|d  |d  |d   d|d
  |d  |d   d|d  |d  |d   d|d  |d
  |d   d|d.  | |d   d|d  |d  | |d   d|d  |d  | |d   d|d  |d  | |d   d|d
  | |d   d|d  |d  |d   d|d  |d  |d  |d   d|d  |d  |d  |d   d| |d  |d  |d   d|d
  |d  |d   d|d  |d  |d  |d   d|d  |d  |d  |d   d|d  |d  |d   d|d  |d  |d  |d   d|d  |d  |d   d|d  |d  |d   d| |d  |d  |d   d|d  |d  |d   d|d  | |d   d|d  |d  |d   d|d  |d  |d   d| |d  |d   d|d
  | | |d   d|d  |d  | |d   d|d  |d  | |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d  |d  |d   d|d  | |d  |d   d| |d  |d  |d   d|d  | |d  |d   d| |d  |d   d|d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d|d  |d  | |d   d | |d  | |d   d|d  |d  |d   d|d  |d  |d  |d   d|d  |d  |d   d|d  |d  |d   d| |d  |d   d|d  | |d   d|d  |d  |d   d|d  | | |d   d	|d  | |d   d| | |d  |d   d
|d  |d   d| |d  |d   d|d  | |d   d.|d  |d   d| |d   |d d< d|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  |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|d.  |d   d1|d  |d  |d   d2|d  |d  |d   d3|d  |d  |d   d|d
  |d   d4|d  | |d   d5|d  |d  | |d   d6|d  |d  | |d   d7| |d  | |d   d8|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?| |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  |d   dF| |d  |d  |d   dG|d  | |d  |d   dH| |d  |d   dI|d  |d   d|d  |d  |d   dJ| |d  |d   dK|d  | |d   dL|d  |d  | |d   dM|d  |d  |d   dN|d  |d  |d   dO| |d  |d   dd|d  | |d   d|d  |d   dP| | | |d   dQ|d  |d   dR| |d   |d df< dS|d  |d  dT|d  |d
   d"|d   dU|d  |d  |  dV|d  |d  |  dW| |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   da|d
  |d  |  db|d  |d  |  dc|d  |d  |  dd|d  | | |  de|d  |d  | |  df|d  |d  | |  dg|d  | |  dh|d  | |d  |  di|d  |d  |d  |  dj| |d  |d  |  dk|d  | |d  |  dl|d  |d  |d  |  dm|d  | |d  |  dn|d  |d  |  do|d  |d   dp|d  |d  |d   dq|d  |d  |d   dr| |d  |d   ds|d
  | |d   dt|d  |d  | |d   du|d  |d  | |d   dv|d  |d  |d   dw|d  |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  | |d   d|d  | |d   d| |d  |d   dQ| | |d   d|d   |d d
< |S (  N)r   r   r   r   r   r   d   r1     r   rA   )     L  r   r   Gm  vU r!     r#   k r    = :    
   X Z e  p$   $  9 @  DH  f  a     L 8 ^   o{) M@ H?   #1 &  , v	 C   j逖   z   2E đ 餭+ 3 钥 gR ?\.Pi @B / O lX TƳ3 mkj E9zfx P w /  vA&ZFX
ʳ+@#Cm	j!鄸Sc|JsH   AW r   iR  0*  z   B/ X	 鰚  0 du+ @m `\ 7#  L 逴  | 5  q g  Q tu  f I 	  頚 @yn : XO       ئ @ j \&   X f|H+J]
 eR 
 =h	 hxx  ^WFdD霦F-/vHr?     XM    L  
 0  xW L&    5M ^x G O  |  P, P	 ¡A j #P    P .c 
"  Z A JU  p \ `Ik C0頍	mYyfAib7  8   l  J# e    \ $  r5   h   餝 9 й  `M/  v \ 3 8 H{ *u Y Q p|li,  f  F  S  <    l    ȯ  H  	 `
 ظ 6n   i(#    骴  P    $ $  Zb  r         r   rG   i<  i  i( iFi  i i i3 i# i? i\B i i
 iΥ i i  i iMi(i  i8Fi7~
iЃ i c i iii  Hi i iT=  i ib r*   i$ i i˺. i`? iE i, iJiQai(Z iѿiK
iwiHi<Xi~8iEi@A i `i02ii i !i i Li Xr0i 7i  Di /i @KLi) i{  iHά iLi iLI ijsAi(Hi1 igi|oiWi~iPuri*x'izvi=
e0i@i}is?/il   	' l   cp l    @z l    C l    8/ i ^_i+ iԵ iО
izui!iE* i,1 il iu`iHj9iXfi>iymiXdli(0L.l   821 l   Q l   xf l    .A l   @w  l   8N	  l    { l   ;q: l    ?U l    V#| l    hW	 i:i\+Yi~SPQiTlRi$"l   iZ& l   lN$ l   NTj il   J t l   u|/" l   .'9 l   e;J l    $ l   / l   {NE i%	ei)ZRi.ic4l   UP< l   J7  l   AKZ  l   <z_ l   b l   Bd<0 l   r~_ l   8l   $d l    Yv" l   ds    %Q iOWl   c,n_ l   K\[l   <rh l   9o7 l   =
 l   %\ l   0]~ l   p]l   nl   ?78l   .xEi8i:  `T  i   K  i ijJ  i i$ in  i i(AF i\   iĻ i K iB!i i% i0icR i "o i@Ġ i{i [i i ظi  iН  if i! 4  i  i$ imi,Y ik iX> ii@ i( il i)ii B i $ i`t
ivli i`i5i i ZiͦLi Wi Ui prb  i iS in[Ci i* iԭiIiPKiV iyiRiؖ>ihiP)l   rO` i ӲVl   
e l   du" l   @,  l   f l     l     i i͚ i<Di2+]"iViq il   : l   $ iml   Xfe l   7n5 l   FW&	 i `l   `f l   r8) i` l   p{& l    # l    C l    02 is i =l   !, l   lSJ i0:'irl   T|`e l   @Nj: l   R2 l   B# l   ,Y3! l   j i~p l   ? l   z% l   vS> l   *(? l   Np^ l    Z
 l   <{ l   ni l   h_( l   &! l   t: l   8$  l   ]! l   T0 l   pv^ l   "=G ii  i> iR i  i i i8 i# i.d i
 iL, iCi  i6i@ .i ui8  iZ i6 iH  ia i1i i iaE i6i* iX	 iN i9iAgiQiX0|
il} i@
i p"*i'i ,iR5i $=ix iӼ i iԏ ih i3	ij/i"Єi`xib;iil   k^ l   " l   pW l   p] l    i m|Mi i*qi{	i4 iiķ`l   hqRD ii5tl   L Q il   B1
 l   Vc l    >E l   X]	 i0ipViЈiHd<bl   =?
 l   0o: l   Vy l   ~re0 i^v$l   } l   lk l   5n< l   DF l   0LG l   ln' l   ~A l   L$j i  i*  i i"  i i   i6 it i@ i e iZu i(" i To i  i  i i  ij
 i id iW ix i iЌR inq ih'C iqi=iOi`\i8	i
ii viN  i$ i ihx i[ iiti.jiti87Xi5& id=i*Di醢 iFu$ii\'i iBi4`Di{5	i̺ziDipPl    }Y iijEi8YiLMl   hvt	 l   		 rKl   8St l   @F iH&  i: i  i< i  iC i(
 i	 i 0 逹* - iH  i&  i. i i, ic i ii i09 i`ii ?i !ih< i iN i1 ijiLQ캃iai 	i~_@ iD iJZ iOQhi	i $i=ixAiFi.Yvi,}Qip  i  ixi  i} i6\ i  i 5   i  ~  iA i  i i> iQ i@KL i	 i~ ih: i'i5i ik
i&  i  i  iW i i i) i'  ijw i i3 ii i iii% ij:i|--iiTiNBig5
"i(i@\vyl   o i@2i 7Xi4  i i¨+ i iR   ie# iJYini*
i. * iiמ	iɬyiai69i|iU=Iihi	`i
;l   k# i`!KBl   | l   L l    IF l   3>N l    |} ic i62 i`i|t
id~%iK6i"W iUiF$l   fV>` l   c" ii-VLl   4Jr l   ,4i
 iE8l   j5	 l   
D	 l   _Tqv l   `0 l   @Z+ l   aC< l   ?t l   @-Y+ l   q{ i ʚ;l    2:" i6i"(l   4W l   KU& iB&iR#l   % l   @3{&& l    a l   >N l   ~X] l   s/ l   4io l   p/35 l    |l l   L)?iol   Py l   wY l   _M+e' l   Epm l   .r1 l   w): l   >!: l   36ud l   YI3 l   8F2b l   )g9Cal    dwSl   ;6[ l   -%>p l   233[ l   CDW l   IU l   Dl   8EK5l    MZYl   W#	C l   =%"-l   [b4A{l   =5l   TS
l   ;l   S6i  i'	 i i1 ix i=iv  i( iAi;i/) ii0idi_ir+iI.i0F!l   ub  i@ xi@dFl     i  ieߗ  i ix- idBi,CiHOi$ i
iWl   i\ i(5
ix l    i Cl    l   o{ iml   < l    z< iԔ iTi6Q%!iqG i+i%iIPiud	is)l   U  l   c%  i|(<l   HV l   tj!1 l   _ l    iW l   @5M i /hYl    KX3 i,i<tl   Au) l   6Oj il   4> l   0I% l   z l    60 l   Lu'/ l   K,; l   F4ti.l   |-; l   r-	 l   T	 l   ]L$ l   iG0 l   Zog* l   KNSRjtl   47l   S_pv l   !l   \$/l   w&6Rl   o6'!l   ^G@l   F>iiMm i& i: i܆) i i? iL| i97Ai2ki9 iiXV.i>i5rd+i)iC#iGiA ik iyʓ idBsi i  iƑ_iԫ2iwq i 	l    i_l   G! l   ? i Ml   Tm	 i,hiʜ i1i8iEiQiZ/l   7S l   1 iNrl   }sw l   a= ingE+l   t@w l   {~ i m0l   X i"iDul   gr l   U l   ,{ l   Yo l   d7 l   QH iqhFl   [R l   P l   = l   0z l   ! lJ l   ^- l   Xy l   W=l   ;gi  i(| i i3A i51 i2 i!	iPij8iaiX	iX	ipLi/ ixa iffiW i#D i{e@i iii8ifl   <A i )i iZiUi Hi%?il   Cp ii5Pl   m i0	l   RD i iQl   %p dEl   c l   {L l   <+ l   )z l   |p16 l   }j ii i i i< i
Y i, iiʉ#i	i"iX i*n+ isgz i`/4 i i}	i. i8iiw|* ii(LiQiRidiXv`gi
iAl   t" l   (
 l   5 i|  i iDB iJ i9 i'O in im i6 iYkizG i i}i7 *iA*Bi5w id:iml   pIe X  i6  i i r'   iT$  i[ i) i,Q iR  iA iRo iOciv6 i? iA iqioin:{ iP i2i8ixAi08 iMwifi8i7siCZ iNi Rbiai*i0&jiX.i ،6i ;aEi@yl    O* i pAvl    PRW iP  i3j i{DO i(!iLV id ib(iigi/
 i族i9ip]i!
s  iy8i&l   1SS l   Fr iHip+ iՙl   : l   )Ms
 l   9V* ii@]l   xr0 l   QDd i g l   oB  i0!jl   :;A i $u*l   9	 l   #4 i  @,l    PAt     04< i ip iyigiR!i50 i$ieP,l   8bn l   AuN i\R0Y i[i'ql   L l   N_ l    2 i`_iS)xVl    l   >;dA l   mH, i 3l   dj
 l   9#pM l    7: l   %9 iY -l   vV# l   rw l   6V"U l   & l   
\3 l   Pki l    8}	 l    T9#< l   @og7 l    	 l    p- i i1iH l   PA l   cS l   .$K inl   U) l   e l   VL1 l   gd)* ill   G_# l   ~ l   BW l   a  l   t1 l   ,y l   7gMl   Kay l   q1F l    d ?l   -l   z$d l   8nU1 l   xVw l   QL l    0# l    AWU l    0ao iqiDl   EG<L l   P l   R@3 i&Gl   &1 l    tn[ l   ,d! l   TIE l   (#A l   &3_ l   /l   $)l   \	A l   *ll   ufKl   ,Tl   (Fx l   ,nl   QMl   RfK l   csl    _q l   a'l    h] iLl   3g
 l   D#3 l   )R& l   6#l   ^Nx l   6-"l   	zCAl   ~y13l   Xy! l   B*>l   Wjl}l   baW4	l   Xrl   y'W l   7 l   (o l    B>l   1/ l   ILl   k[l   "#fzl   &~\l   3l   }9
l   `=AK
l   l   o6l   f]ql   :_l   cGNl   o l   nJJl   ub]l   dUl   HxGUl   mTl   GBal   ? pl   *#l   e`Tii6  i, iH i   i iݾ i3E in  i i iiU i=3 ioi;iB5i i\iGi3Bi i6 i%?i6F&i)	ihi`i9i`miE?iX<#ipl    OM l    x iL| i1' i'F i{  i?1 i]ii*/i܇ ii$ci(7idixt i	i:i}7i.i]i2#Sl    L i,|qiq(l   #N l   /k l   d  l   #8c l   1 l   `YkD l    Ql l   pL,-     HNZ i& iD$ iB i9K i0Ni{ir i i?i7@ ivri\ihim i
riZ!l   eBv iNb	id	ippiO,l   %V l   E i8Jl   xRU l   :i l   /8 l   P- l   @5 l   24_QF l    
b l   yb l   "3<L l   %\+ l    Xp7 l    hC! iE iևi#l   i  iidij@i<zsl   JCV
 l   }K	 l   PLi	 iFĥOl   0 l   #:5 l   
,\ l   >s=
 l   gJ l   AI@g l   |6D+ l   6*l   3v{ l    y#D l   `"9 l   g l    Q i{T iO l   FI l   *N# l   90% i{l   'p l   ~_? l   D l   $C/y l   3 l   c7l   rSg)l   H&M l   J/ l   $MF? l   RC= l   4cl   `W l   (=S&l    sO ihl   `z l   ]r7 l   |dzd l   $9 l   &Ol   t~l   =2{ l   *7D l   '_qdl   Gl    }tl   Mxb l   .vs l   "E$l   1%D l    l   |cp l   /	l   j{i l   hL/ l   !W0l   b=Al   ?l   X|l   e l   k8 i~  i:3 iP   í i i$T iJy  i iZf iZi+ ijhiaX
i
 i,! i 8i;ͻi6'iO{ii
iP7)i`lid1i@>i ZUl     i i-6 iW iT i@ ii8`
逨ij iih7ii iJl     iܭSi l   |c l   ~m2 l   g*T- i Ll   I3 l   W l    Uw l    Y|I l    :@     GP i2* ii8ii8BiW iOi/Fid-ipoir9i'?ihl   J l   X;=o i!l   Ud i=$l   V
 l   rO l   4] l   eto? l   vFe	 l   `3A l   -' l   1b l   'y% l    c i.= iQv'i/l   t4NA i`XiCl   T] l   X l   txg l   oL l   ]
) l   ETOC l    qx; l   hHc l   X1f l   1 l   OZ< l    v|o l    ofZ i.(itl   +5, iPinbl   ,_	 l   .?o?3 l   (B8 l   %W
 l   Ehr l   ?K l    l   PgS l   P9 l   <6Rl   3Ln l   5 l   xoq2 l   `[$ l   M l   (,1l   >ll   P#
l   vl   h* l   ZY l   m&C l   >CWl l   GM\l   / Y% l   	Kh l   v zEl   )<=ql   y iH  i i  i i  iX*n v/  i
 i iHiT i
 i iC:i&yi: ii˖ii	ii >ii	%i$ iy2@ i6 i  it+ i2iaiai6 i'{iDi{Oi4i|(ivciǫ'iPVl   Hw l   M. i geQl   i^ 逺>i. iݕiiiHYO i;iB	iuhsi|;i&i=o,im(l   f iL\#l   &!< l   2p l   )E l   }1 l   C^a	 l    ~c l   Ex
 l   $q iǔiZl    x l   4; ijl    l   T8k
 l   I]0 l   XyV" l   ]H/ l   K(N l   <
 l   4A l   6>9 iܶi$$)l   bd l   |W	 il   *s' l   ^N l   	zf) l   ):UF l   P$` l   ;?yU l   q$ l   uW	 l   :`6# l   2?Fk, l   
,E l    l   ZV l   I) l   1Q\3 i    i  i' iX> iQ i|r/ iF i iKw iwiH i8ii=@ i` igiiH3 ioU s i^  ib i	 i4il ii6i$3iiiJN%iei0ZiMi N@:ii iu ifKi* iTii%ii+i,Ki$l    hR ili gOBl   `L" iMtSipHYi(`Ti̊KIifUVl   0p~ l   P~` l   @0 ii5z
ieQl   sTX l   hlm l   {vc	 l   P\0F l   ZV i7el   Z4 ii
	 i  i^
 iD+ i? i i i^ iy& i) i)S i RWiD io ik iw iWʍ i^ixl8iw iy2;i?i ii@`4<iH( iם ioEigi i&ixi,5i	(iX(ici ei>|}	ihx&ii @ij =i`7iGi)i|;iVMD)5:r   r   r   r   )r   r   r   r   r   br   r   r   rr  &   s          f      p                          ^               t                  j                                                `                            b                                                                  zPolyQuintic.bc                 C   sZ  | j | j| j| jf\}}}}dgd }d|d  |d  d|d  |d   d|d	  |d
   d|d  |d  |  d|d  |d  |  d|d  |d  |  d|d  |d
  |  d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d
  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d	  |d  |d   d| |d  |d   d |d
  |d  |d	   d!|d  |d	  |d	   d"|d  |d  |d	   d#|d  |d  |d	   d$|d  |d  |d	   d%|d  |d  |d   d&|d  |d	  |d   d'|d  |d  |d   d(|d  |d  |d   d)|d  |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  |d   d2|d  |d	  |d   d3|d  |d   d4|d	  |d  |d   d5| |d	  |d   d6|d  |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  | |  dA| |d  | |  dB|d
  |d  |d  |  dC|d  |d  |d  |  dD|d  |d  |d  |  dE|d  |d  |d  |  dF|d  |d  |d  |  dG|d<  | |d  |  dH|d  |d  |d  |  dI|d  |d  |d  |  dJ|d  |d  |d  |  dK|d  |d  |d  |  dL|d  |d  |  dM|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  |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  |d   dc|d  |d  |d   dd|d  |d  |d   de|d  |d  |d   df|d<  |d  | |d   dg|d  |d	  | |d   dh|d  |d  | |d   di|d  |d  | |d   dj|d  |d  | |d   dk|d  | |d   dl|dm  |d  |d   dn|d  |d  |d  |d   do|d  |d	  |d  |d   dp|d  |d  |d  |d   dq|d	  |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  |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  |d   d|d  |d  |d  |d   d|d  |d	  |d  |d   d|d  |d  |d   d|d  |d  |d  |d   d|d	  |d  |d   d|d	  |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   d| |d  |d   d|d
  | | |d   d|d  |d  | |d   d|d  |d  | |d   d|d  |d  | |d   d|d  |d  | |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d  |d  |d  |d   d|d  |d  |d  |d   d|d  |d  |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d	  |d  |d  |d   d| |d  |d  |d   d|d  | |d	  |d   d|d  |d  |d	  |d   d|d  |d  |d	  |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d  |d  |d   d|d	  | |d  |d   d| |d  |d  |d   d|d  | |d  |d   d| |d  |d   d|d<  |d	   d|d  |d  |d	   d|d  |d	  |d	   d|d  |d  |d	   d|d  |d  |d	   d|d  |d	   d|d  | |d	   d|d  |d  | |d	   d|d  |d	  | |d	   d|d	  |d  | |d	   d| |d  | |d	   d|d  |d  |d	   d|d  |d  |d  |d	   d|d  |d	  |d  |d	   d|d  |d  |d  |d	   d|d  |d  |d	   d|d  |d  |d  |d	   d|d  |d	  |d  |d	   d|d  |d  |d	   d|d  |d	  |d	   d|d	  |d  |d	  |d	   d| |d	  |d	  |d	   d|d  |d  |d	   d|d  |d  |d  |d	   d|d  |d  |d	   d|d  |d  |d	   d| |d  |d	   d|d  | |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  | | |d   d|d  |d  | |d   d|d  |d  | |d   d|d  | |d   d|d  | |d  |d   d|d	  |d  |d  |d   d| |d  |d  |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d  | |d	  |d   d|d  |d	  |d   d| | |d  |d   d|d  |d   d|d  |d  |d   d|d	  |d	  |d   d| |d  |d   d|d  | |d   d|d  |d  | |d   d|d  |d	  | |d   d|d  |d  |d   d|d  |d  |d  |d   d|d	  |d  |d   d|d	  |d  |d   d| |d  |d  |d   d|d  |d	  |d   d|d  |d   d|d  | |d   d|d  |d  |d   d|d  |d   d|d	  | | |d   d| |d  | |d   d|d  | |d  |d   d| |d  |d   d|d  |d   d|d  |d  |d   d|d  | |d   d|d  | |d   d| |d  |d   d| | |d   d|d   |d< d|d  |d  d|d  |d   d|d  |d   d|d  |d
   d|d  |d  |  d|d  |d  |  d|d  |d  |  d|d  |d  |  d|d
  |  d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d	  |d  |d   d| |d  |d   d|d
  |d  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d |d  |d  |d   d|d  |d  |d	   d|d  |d	  |d	   d|d  |d  |d	   d|d  |d  |d	   d|d  |d	   d|d  |d  |d   d|d  |d	  |d   d|d	  |d  |d   d	| |d  |d   d
|d  |d  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d	  |d   d|d  |d   d|d	  |d  |d   d| |d	  |d   d|d  |d  |d   d|d  |d  |  d|d  |d  |  d|d  |d  |  d|d	  |d  |  d| |d  |  d|d
  |d  | |  d|d  |d  | |  d|d  |d  | |  d|d  |d  | |  d|d  |d  | |  d=|d<  | |d  |  d|d  |d  |d  |  d|d  |d  |d  |  d|d  |d  |d  |  d |d  |d  |d  |  d!|d  |d  |  d"|d  | |d  |  d#|d  |d  |d  |  d$|d  |d  |d  |  d%|d	  |d  |d  |  d&| |d  |d  |  d'|d  | |d	  |  d(|d  |d  |d	  |  d)|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	   d|d  |d  |d	   d|d  |d  |d	   d| |d  |d	   d|d  | |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | | |d   d|d	  |d  | |d   d| |d  | |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d  | |d  |d   d|d  |d  |d   d| | |d	  |d   d|d  |d   d|d  |d  |d   d|d  |d	  |d   d|d  | |d   d|d  |d  | |d   d|d	  | |d   d|d	  |d  |d   d| |d  |d  |d   d|d  |d  |d   d|d	  |d   d|d	  | |d   d| |d  |d   d|d  | | |d   d| |d  |d   d|d  |d   d|d  |d   d| | |d   |d	< d|d  |d  d|d  |d   d|d  |d   d|d
   d|d  |d  |  d|d  |d  |  d|d	  |d  |  d| |d  |  d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  |d  |d	   d|d  |d	  |d	   d|d	  |d  |d	   d| |d  |d	   d|d  |d  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d	  |d   d|d  |d   d|d	  |d  |d   d| |d	  |d   d|d  |d  |d   d|d  |d  |  d|d  |d  |  d|d  |d  |  d|d  |d  |  d|d  |d  | |  d|d  |d  | |  d|d  |d  | |  d|d  |d  | |  d|d  | |  d|d  | |d  |  d|d  |d  |d  |  d|d  |d  |d  |  d|d	  |d  |d  |  d| |d  |d  |  d|d  | |d  |  d|d  |d  |d  |  d|d  |d  |d  |  d|d  |d  |d  |  d|d  | |d	  |  d|d  |d  |d	  |  d|d  |d  |d	  |  d|d  |d	  |  d|d  | |d  |  d|d	  |d  |d  |  d| |d  |d  |  d|d  | |d  |  d|d  |d  |d  |  d|d  | |d  |  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  |d   d|d  |d	   d|d  |d  |d	   d|d  |d	  |d	   d|d  |d  |d	   d|d  | |d	   d|d  |d  | |d	   d|d  |d	  | |d	   d|d  | |d	   d|d  |d  |d	   d|d	  |d  |d  |d	   d| |d	  |d  |d	   d|d  |d  |d	   d|d  |d  |d  |d	   d|d  |d	  |d	   d|d  |d	  |d	   d| |d  |d	   d|d  | |d   d|d	  |d  |d   d| |d  |d   d|d  | | |d   d |d  |d  | |d   d!|d  | |d  |d   d"|d  |d  |d   d#| | |d  |d   d$|d  |d   d%|d  |d  |d   d&|d	  |d   d'|d	  | |d   d(| |d  | |d   d)|d  |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  |d   d5|d  |d	  |d   d6|d  |d  |d   d7|d  |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@|d  |d  |d   dA|d  |d	  |d   dB|d  |d   dC|d	  |d  |d   dD| |d	  |d   dE|d  |d  |d   d|d  |d  |  dF|d  |d  |  dG|d  |d  |  dH|d  |d  |  dI|d  |  dJ|d  | | |  dK|d  |d  | |  dL|d  |d  | |  dM|d	  |d  | |  dN| |d  | |  dO|d  | |d  |  dP|d  |d  |d  |  dQ|d  |d  |d  |  dR|d  |d  |d  |  dS|d  | |d  |  dT|d  |d  |d  |  dU|d  |d  |d  |  dV|d  |d  |  dW|d  | |d	  |  dX|d	  |d  |d	  |  dY| |d  |d	  |  dZ|d  | |d  |  d[|d  |d  |d  |  d\|d  | |d  |  d]|d  |d  |  d6|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   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	   d|d  |d  |d	   d|d  |d	  |d	   d|d  |d	   d|d  | |d	   d|d	  |d  | |d	   d| |d	  | |d	   d|d  |d  |d	   d|d  |d  |d  |d	   d|d  |d  |d	   d|d  |d  |d	   d| |d	  |d	   d|d  | |d   d|d  |d  |d   d|d  | | |d   d|d  | |d   d| | |d  |d   d|d	  |d   d| |d  |d   d|d  | |d   d|d  |d   d| |d   |d< d|d  |d  d|d  |d   d|d  |d   d|d  |d	  |  d|d  |d  |  d|d  |d  |  d|d  |  d|d  |d  |d   d|d  |d	  |d   d|d	  |d  |d   d| |d  |d   d|d  |d  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d	   d|d  |d	  |d	   d|d  |d	   d|d	  |d  |d   d| |d	  |d   d|d  |d  |d   d|d  |d  |  d|d  |d  |  d|d	  |d  |  d| |d  |  d|d  | | |  d|d  |d  | |  d|d  |d  | |  d|d  |d  | |  d|d  | |d  |  d|d  |d  |d  |  d|d  |d  |d  |  d|d  |d  |  d|d  | |d  |  d;|d	  |d  |d  |  d| |d  |d  |  d|d  | |d	  |  d|d  |d  |d	  |  d|d  | |d  |  d|d  |d  |  d|d  |d   d|d  |d  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d|d  |d  | |d   d|d	  |d	  | |d   d| |d  | |d   d|d  |d  |d   d|d  |d  |d  |d   d|d  |d	  |d  |d   d|d  |d  |d   d|d  |d  |d  |d   d|d	  |d  |d   d|d	  |d	  |d   d| |d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  | | |d   d|d  |d  | |d   d|d  | |d   d|d	  | |d  |d   d| |d  |d  |d   d|d  | |d  |d   d| |d	  |d   d|d  |d	   d|d	  |d  |d	   d| |d	  |d	   d|d  | |d	   d|d  |d  | |d	   d|d  |d  |d	   d|d  |d  |d	   d| |d  |d	   d|d  | |d   d|d  |d   d| | | |d   d|d  |d   d| |d   |d< d|d  |d  d|d  |d   d|d   d|d  |d	  |  d|d	  |d  |  d| |d  |  d|d  |d  |d   d|d  |d	  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d	  |d   d|d  |d   d|d	  |d  |d	   d| |d	  |d	   d|d  |d  |d   d|d  |d  |  d|d  |d  |  d|d  |d  |  d|d  | | |  d|d  |d  | |  d|d  |d  | |  d|d  | |  d|d  | |d  |  d|d	  |d  |d  |  d| |d  |d  |  d|d  | |d  |  d|d  |d  |d  |  d|d  | |d	  |  d|d  |d	  |  d|d  |d   d |d  |d  |d   d|d	  |d	  |d   d| |d  |d   d|d  | |d   d|d  |d  | |d   d|d  |d	  | |d   d|d  |d  |d   d|d  |d  |d  |d   d|d	  |d  |d   d	|d	  |d  |d   d
| |d  |d  |d   d|d  |d	  |d   d|d  | |d   d|d  |d  |d   d|d  |d   d|d	  | | |d   d| |d  | |d   d|d  | |d  |d   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    rO  rU   i0\  r1   r*   r   r   rW  i`  rL   r   ie iR< r   i r!   i0 i, rA   i`ir#   ii r   iz~ i>iUir iܤi$(isNl   9 i` iO.l   < l   r iil   W l   l^ i3_i@tl   `o l   `nP' l    _ l    2D7 l     w l    G$	 l    p r`  i  i v
 i iP~>irrG   r_  i{ iy i5i\ji(C ir@xiYl   ^P( l   -nT
 i  ii0˫!l   m l   Ri! icg/iGit\ĩil   %t10 l   3w iBhIl   @A l   $ l   rR l   M	 l   @h|6 l   S l    TD) l    rj! l    u: l     h18 l     ~ l    ?" l    `O8 l    `Z, id	 iT iR9iGiLAi8+3 iBmi6:zl   @*)8 l   f,X= ipYzRi# r'   i4i5l   T{bW l   87 l   bHC% iål   Px l   M` l   ~i6* l   (Nkl   1J l   PQB" l   ;IT l   +cHl   Lr l   @8)i l   <d l   Tgl    	,K l   @Vx l    rKdl   WD;nl    Sel    8l    ry)l    lx:l    pbl    P'i^! i~i
l   P,	 l   fP l   TOj iYxi_2l   P@ l   @, l   ]Ai`%	l   H; l   (5@l   xp,l   )=l   0~7 l   T,l   ?Lcl   D`GM l   @1e l   0I>l    Mx;l   ?@Ll   ~`l   `	+

l     l    ^04l    ,Hl|l    `%K]ihi
5Ol   = l   ,j l   jrl   H%d: iؐ]*l   * l   `$l   SEl   `$l   t l   Q0 l    FIhl   -MJ8l   A}%@l   ODl   *g %<l   pl   `%lYl   3(\5l   0Kl   yBl   1'd|l    ~F$+l    TiN&l    `wl   J=iU
 l   t= l   -	l   pFl   gYl   b]l   kXrl   Z#El   (bl   cisl   
0l   a|&l   08sHg l    Wl   `n<#xl    R$ l   =tW l   hl   wY>K
l   ]
l   _=D l   "n2l   sh0O l   g=rl   4X
 l   <*.xl   LLO7 l   D@9 l   `.P5 l    BR$l   U	l   `pL)l   k2lo	l   I2U+ l   PcppkH l    h;i l    6Xal   &l   l'M&+X l   TTH  l   =.9 l   xkSl	 l   .F r/   i@Q  i,  iN rF  iPy i i3( iJ( iP' iU i_ i&O ir^  i\6 ii i\i1 ii;P0ib%ji?ixUi%iol   l# iRi<3l   8|, i b&l   }x l   }) i el    E0e rc  rG  i` i  i!pilri igT id8 i{vi}Bixi<Ԥi9l   B;	 iD:9i0eiil'Gihl   <T	 l   v
7* iЭl   X[ l   D0? l   Ir
 l    a
i l   07 l   oO, l   (3 l    FU l   *l( l   b( l     f l    Mj9 l    0( l    PC is il=) ieNiU i$&`ihYra  it+ i$Kl   4[7 l   !Glh
 l   bD ipޟiNi5txl   J@r l   pji~ ixI;l   # l   	g l   @&{f)l   >d}/ l   xv` l   /+/Z l   RSl   {*l   aY l   y,l   8n=l    Qjl    #$
l   l     q0l    pe.l    8;iP4ziL=^'l   += l   r l   ;Xjb iU1l   y6 l   2d% l   JRg l   0!q0 l   ;eE l   RG~ l   M	=_ l   $fl   _p l   G<l   jmXl   U@l    [Al   HqX
l   3tl    bfQl    Tl= l    P0iH0l   Ge$ l   $qb l   8Sl   6r=l   N|A l   d;E l   #3l   9	l   :\: l   cXl   -Oi!l   8M; l   @>Em l   &}*<l   y/Tl   pN~)l   pEel   Yl   @Ge,l    5!%l   l*  l   02Xl   h+zl   )
iU0Sl   +Ul   "il   *"l   1D l   h<l   o^~^l   P<_| l   m|#fl   rCGKl   |j<l   -'|l   LVR(l   Zf;l   xZcl   "2 l   Rl   @8V= Ql   5$WOl   ag; l   2dRl   |X{hx l   H{bcDl   dZ8 l   67@i
  i  iP i i@j  i(
 iVaW i i# i7+ i-i%rH  i8A i!ii@0it! iDdi/iecFi$uiм}6l   . il    *)V l   ts i@8Mll    ! rf  i| i iGi iŮ iHci9WSiNi8 i/Z i	iV
l   0f i iz)iRl   
j ix@QiLfJi0Yl   Z iCil   P W l   *c l   @[! i NrSl    F))$ i\ iwI i%)0iR<l    rK  i
i9Al   u#k
 l   $I iCi%l   HLD l   }~X l   B|E
 i|gl   dk  l   
R l   ;bwp l   > l   `N l   jl   p>N l   @,l   t7xl   Bl    A{l    	WP{ihiLl   C l   KDB l   @& i$h5l   r4 l   Z=M l   gCl   Bm l   lq*l   Fl   T=5 Il   $2Zl   72l   e(l   pKHMl   @Nl    Vil   o l   iW\ l   ?k l   Z}@ l   r(7] l   '$al   K Wl   PAM l   0vl   #hl    l   $l   Hl   q>l    SzGl   4-~ l   QXTl   A18 l   89l   
A&l   4l   1: 6l   J
ul   c{ l   ?B0"l   tqXl   cl   A8Xav l   )l   Q-l   	$W\l   KD l   4&Ei#  i0 @8  i i\ ih rU  i` iTE ii $qit i iA/2ioiJ@ iX
iu	&rY  i1i)|"i`ikri  iQ iaMQ iJiH i` iT i5i
i0FiPg i9/iddiYi_iccAi'l   V i0*;l   vr l   e# l   : i0i Sel    Ic	 i iii
*i5iUi?ziuO-l   Pn il   Et: l   F( l   13k l    l   
G( l   }0L l   &F( l   Pd l   4 "\ l    ^	 l    77m l   } in$7	l   N|
 l   A3 l   S,  l   X1G l   ai? l   "yr l   B.2E l   k6jl   AP* l   CAUl   PvpGtl   %tUl    !p< iP l   l l   ( l   .= l   6Y9 l   J< l   Yal   \P l   yAhl   uml   J?~l   X,Dl    vu l   k/l   fl   /Jwl   	<l   Nlk l   Fl   <kl   ,x571l   RIiT  ipb  iG i3 iW i|  i i.ii iaiN:ViD#i
iAi irl  i  i i$<i0 il iiiam i1i#iivi3iހip5}il   F8 io iai4i
i& d?M iƀu*l   _: i|Ol   TO&* l   Rx l   Pa l     K l   it l    V@( l   {Y l   QU$ rm  i(iuzl   I{@ l   *1* l   8e l   g;" l   hb l   b14 ihCl   N l   : l   8Y] l   1sI l   @F l   Y-'$| l   v*Rl   \!U l   P9N l   'l   R- l   C=sr   ii= ig iK ixp i i8 iJVi~# i!wre  iiTqro  id  i ib* i3 iÝS i>GiPi i1i߿Di wi4Mi*diZiJz ieiS"i$i|<i0i1pi<<1l   # l   tzr l   pY!V l    rT l   MO itl   &X^ l   B l   uC l   9 l   l l   %] i)scl   Y l   g?9 l   W l   T`> l   2eFp l   s6 rq  )r   r   r   r   r   or   r   r   rv  ]   s   
                        f                                                                zPolyQuintic.oc                 C   s  | j | j| j| jf\}}}}dgd }d|d  |d  d|d  |d   d| |d	   d
|d  |d  |  d|d  |d  |  d|d  |d  |  d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d|d  |d  |d   d|d  |d  |d   d| |d  |d   d|d  | |d   d|d  |d  |d   d|d  |d  |d   d|d  | |d   d|d  |d  |d   d|d  |d   d |d  | |d   d!| |d  |d   d"|d  | |d   d#|d  |d  |  d$|d  |d  |  d%|d  |d  |  d&|d  |  d'|d  |d  | |  d(|d  |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  |d  |  d2|d  |d  |  d3|d  |d  |  d4|d  |d  |d  |  d5| |d  |d  |  d6|d  |d  |  d7|d  |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  | |d   dA|d  | |d   dB|d  | |d  |d   dC|d  |d  |d  |d   dD| |d  |d  |d   dE|d  | |d  |d   dF|d  |d  |d  |d   dG|d  | |d  |d   dH|d  |d  |d   dI| | |d  |d   dJ|d  |d   dK|d  |d  |d   dL|d  |d  |d   dM| |d  |d   dN|d  | |d   dO|d  |d  | |d   dP|d  |d  | |d   dQ|d  |d  |d   dR|d  |d  |d  |d   dS|d  |d  |d   dT|d  |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   da|d  | |d   db|d  | |d   dc| |d  |d   dd| | |d   de|d   |d< df|d  |d  dg|d  |d   dh|d  |d  |  di|d  |d  |  dj|d  |  d$|d  |d  |d   dk|d  |d  |d   dl| |d  |d   dm|d  | |d   dn|d  |d  |d   do|d  |d  |d   dp|d  | |d   dq|d  |d  |d   dr|d  |d   ds|d  | |d   dt| |d  |d   du|d  | |d   dv|d  |d  |  dw|d  |d  |  dx| |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|d  |d  |d  |  d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | | |d   d|d  |d  | |d   d| |d  | |d   d|d  | |d  |d   d|d  |d  |d  |d   d|d  | |d  |d   dH|d  |d  |d   d| | |d  |d   d|d  |d   d|d  |d  |d   d|d  |d  |d   d|d  | |d   d|d  |d  | |d   d|d  | |d   d|d  |d  |d   d| |d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  |d   d|d  | | |d   d| |d  |d   d|d  |d   d|d  |d   d| | |d   |d< d|d  |d  d|d  |d   d|d   d|d  |d  |  d|d  |d  |  d| |d  |  d'|d  | |d   d|d  |d  |d   d|d  |d  |d   d|d  | |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  |d   d|d  | |d   d'|d  |d  |  d|d  |d  |  d|d  |d  |  d|d  | |  d|d  |d  | |  d|d  |d  | |  d|d  | |  d|d  |d  |  d|d  |d  |d  |  d| |d  |d  |  d|d  |d  |  d|d  |d  |d  |  d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d  |d   d| |d  |d   d|d  | | |d   d|d  |d  | |d   d|d  | |d  |d   d|d  |d  |d   d| | |d  |d   d|d  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  | |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| | |d   d| |d   |d< d|d  |d  d| |d   d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  |d   d|d  | |d   d|d  |d  |  d|d  |d  |  d|d  |  d|d  | |  d|d  |d  | |  d| |d  | |  d|d  |d  |  d|d  |d  |d  |  d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d  |d   d|d  | | |d   d|d  | |d   d| | |d  |d   d|d  |d   d| |d  |d   d|d  | |d   d|d  |d   d| |d   |d< d|d  |d  d|d  |d   d|d  | |  d|d  |d  |  d|d  |  d|d  | |d   d| |d  |d   d|d  | |d   d|d  |  d|d  |d  |  d| |d  |  d|d  | |  d|d  |d  | |  d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d   d| | | |d   d|d  |d   d| |d   |d< d|d  |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    ir1   rJ   r   rA   rK   rL   rM   r   r   rN   rO   r!   rP   r#   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   i  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   ir   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  i  r  r  r  r  r  r  r  r  r  r  r5   r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  ir(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r   r9  r:  r;  r<  r=  r>  r?  r@  rA  rq  )r   r   r   r   r   ar   r   r   rw  p   s>   
        b      l        zPolyQuintic.ac                 C   s3  | j | j| j| jf\}}}}dg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  |  d&|d  |d  |  d'|d  |d  |  d(|d  |d  |d  |  d)| |d  |d  |  d*|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  | |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   d|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   d|d  |d  |d   d| | |d  |d   d|d  |d   d|d  |d  |d   d|d  |d  |d   d|d  | |d   d|d  |d  | |d   d|d  | |d   d|d  |d  |d   d| |d  |d  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  |d   d|d  | | |d   d| |d  |d   d|d  |d   d|d  |d   d| | |d   |d< d|d  |d  d|d
   d|d  |d  |  d| |d  |  d|d  |d  |d   d|d  |d  |d   d|d  | |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  |d   d|d  | |d   d|d  |d  |  d|d  |d  |  d|d  |d  | |  d|d  |d  | |  d|d  | |  d|d  |d  |  d|d  |d  |d  |  d| |d  |d  |  d|d  |d  |  d|d  |d  |d  |  d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d  |d   d| |d  |d   d|d  | | |d   d|d  |d  | |d   d|d  | |d  |d   d|d  |d  |d   d| | |d  |d   d|d  |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  | |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| | |d   d| |d   |d< d|d  |d  d| |d   d	|d  |d  |  d
|d  |d  |  d|d  | |d   d|d  |d  |d   d|d  |d   d|d  | |d   d| |d  |d   d|d  | |d   d|d  |d  |  d|d  |d  |  d|d  |  d|d  | |  d|d  |d  | |  d| |d  | |  d}|d  |d  |  d|d  |d  |d  |  d|d  |d  |  d|d  |d  |  d|d  | |d   d|d  |d  |d   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    ir   rL   i  r!   r   i  rA   i-  r#   i  i  r1   ie|  r   iQ  i%  r   i  iow iX  id i ih  rt  rU   i- iM i  i  i uX i@ i ' i Hq i s# i @ i  i @ i  i  i r*   i  i i i2 i5% i i i i.E i"iuOE rE  iP! i;zi i  ih: i`l ipYi ; i iii  i  0i ` r   i  i i'H' i$ iw ihN i-iOi( iC iw?iiݧ iH:i.t	iii i8i ӌ	i@i '	i 'i HiW i  iR r\  ih i imi@id Ci~ i,i<}%iipLki@!icM)i!xi4iNi `!i wGi 8i i iiV0iKiIܗiV'i)i~I iF=Kiji@к%i\Ki@ɫ@l    ;A ii]Vi0i^в iI*i!bl    l   (ajT l   <{n} l   `A l   P&f= iNhiiPi!]l   6X l   y] rZ  ihl   FYz l   )W  rD  r   rF   n   i8  i0  i  iC  i"  i)  i i  ib  i i i  i@B  i0s i i   i` i@U i H i m i, i ~ i  iH  i  id_  i  io i7 i89 iX  ib iT, iT i2  ii ipf igi iY ieiUi  i@i/i 9 i ,"i $iz  ip i2
 i^ rI  i
 ip i i0 iV iĲL iti rJ  i6Qii@Ό
i %i _L	iܪ  i. iC i! i(\ix ii*i V	i,ip rR  i`	i`(Ci9i@Vi"i 4I#i, i&i:t ii iRipDi*r~ivl   /w i& ie'idOiiL5(i^_ l   twb r   i6/_;l   @7t l   T+  r[  rp  P   r]  i  i  iQ  i  i  iK i i  iL i4 i i8 i i + ik i ~ i
  i  i id  ix i  ix  i i@ ia  i iJ(i> i` iP iȣi i@ai  i  i> i  i i+ iw ii iU1 iiR)NiHixrS  iЭiOrh  i i, i i' i iΏi܈id
iGAi8	ipi@	i Irn  i_iFiG.id#/iwQii*SOi^siRgjix rN  ix   i*  i   i#  i  i  i   iְ  rT   i  ir iy  i`C iX i i i ." i  i;  i  i#  i( iR rj   i& i&& i;! rs  ix> i  iN i T i 	 rP  i~	  i  i<[ i:* rG  i iD ipUI iT ir  rx   rb  ii ie iZ{f iHpiMli	ii$7i,iixoi@	i7r  iiPr.   i"  i  iO  iZ  i8 i  i * i S i  i  i i  i< i i@d i@' i8 i'	 r/  i iV- i"} iz# r   ix+ i` rM  rV  ie ru  i! i@ i ip89 i\$r   i+  rg  rd  i   i3  rL  i  i  r   i i rf   n i iD rT  r  rQ  i%& iNrS rq  )r   r   r   r   r   cr   r   r   r|     sr   
              ~            8         <          h   zPolyQuintic.cc                 C   s  | j | j| j| jf\}}}}d|d  |d  d|d  |d   d|d   d|d	  |d  |  d
|d  |d  |  d| |d  |  d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d  |d   d|d  |d   d|d  |d  |d   d|d  |d  |  d|d  |d  |  d|d  |d	  |  d|d  | | |  d|d  |d  | |  d|d  |d  | |  d|d	  | |  d|d	  | |d  |  d|d  |d  |d  |  d| |d  |d  |  d |d  | |d  |  d!|d  |d  |d  |  d"|d  |d   d#|d	  |d  |d   d |d  |d  |d   d$| |d  |d   d%|d  | |d   d&|d  |d  | |d   d'|d  |d  | |d   d(|d  |d  |d   d)|d  |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    ;   r#   r      rU   $   r1   io  i2
  Q   r!   i  r   iI*  rj  i\D  r@   i'  r>   i0  iD  i  rA   i%  i  r9  r   iTi i~  i`  r<  i  rg  r6  i1G  i iK iX iP i	=  i r{  i rk  i i i}) r!  iT* i rX  rq  )r   r   r   r   r   Fr   r   r   r     s       zPolyQuintic.Fc                 C   s$   | j }| j}t|t|| }|S N)r  rw  r   r	   eval)r   thetar  rw  l0r   r   r   r     s   zPolyQuintic.l0c                 C   s   | j }dgd }| j}t|d t| d|  |d< t|d t|d| |  |d< t|d t|d|  |d< t|d t|d| |  |d< |S )Nr   r   r   r!   r#   r   )r  rr  r   r	   r  )r   r  dr  Trr  r   r   r   r     s   
"$ $zPolyQuintic.Tc                 C   s,   | j }| j}t|t|||  }t|S r  )r  rv  r   r	   r  r   )r   r  r  r  rv  orderr   r   r   r     s   zPolyQuintic.orderc                 C   sD   | j }| jtdd }t|t|d| | j  }t|t|fS )Nir!   )r|  r   r   r   r	   r  r  r   )r   r  r  r|  uvr   r   r   uv   s   zPolyQuintic.uvc                 C   s   | j | j| j| jgS r  )r   r   r   r   )r   r   r   r   zeta   s   zPolyQuintic.zetaN)__name__
__module____qualname____doc__r   propertyrH   rr  rv  rw  r|  r  r  r  r  r  r  r   r   r   r   r
      s*    

6



r
   N)r  
sympy.corer   sympy.core.evalfr   sympy.core.numbersr   r   sympy.functionsr   sympy.polys.polytoolsr   sympy.utilitiesr   r	   r
   r   r   r   r   <module>   s    