o
    oh۝                     @   s   d Z dd dd dd dd dd dd gdd d	d d
d gdd dd dd dd dd dd gdd dd dd dd dd dd gdd dd dd dd dd dd dd dd dd d d g
d!Zd"S )#zDLookup table for Galois resolvents for polys of degree 4 through 6. c                 C   s   d|  | d|  S )N    s1s2s3s4r   r   }/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/polys/numberfields/resolvent_lookup.py<lambda>	       r
   c                 C   s`   d| d  | | d |d   | d |  d|  | |  d|d   d| |  d|d   S )N               r   r   r   r   r	   r
   
   s   ` c                 C   s   d| 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      
   r   r      6       8   r   r   r   r   r	   r
      s   b 
c                 C   s  d| d  | | | d |d   d| d  | |  d| d  |d  |  d| d  | |d   d| d  |d   d| d  |d  |  d	| d  | | |  d
| d  |d   d| d  |d  |  d| d  |d  |d   d| d  | |d   d| d  |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   r      r         r         r   !   H   $   0   t      r   x   `   @   r   r   r   r   r	   r
      sN   f 

c                 C   s  d| d  | | | d |d   d| d  | | |  d| d  |d   d| d  |d  |  | d |d  |d   d	| d  |d  |  d
| d  |d  | |  d| d  | |d   d| d  | |d   d| d  |d  |  d| d  |d  |d   d| d  |d  |d   d| d  | |d  |  d| d  |d   d| d  |d   | d |d  |  d| d  |d  | |  d| d  |d  |d   d| d  | | |d   d| d  |d  |  d|  |d  |d   d|  |d  |d  |  d|  | |d   d|  |d  |d   d|d  |  d|d  | |  d|d  |d   d|d  | |d   d| |d  |  d|d   d| |d   S )Nr   r   r   r   r   r   r   r      <   r      &   	   r   r            "   i   h   r#      P  r$      r   r   r   r   r	   r
      sn   f 
c                 C   sT  | d |d  d| d  | |d   d| d  |d  |  | d |d  | |  d| d  | |d   d| d  |d  |d   d	| d  | |d  |  | d |d
   d| d  |d   d| d  |d  | |  d| d  | | |d   d| d  |d  |  | d
 |d  |  d| d
  |d  |d   d| d
  |d  |d  |  d| d
  | |d
   d| d
  | |d   d| d
  |d  |d   d| d  |d
  | |  d| d  |d  |d   d| d  |d  | |d   d| d  | |d  |  d| d  |d   d| d  | |d   d
| d  |d  |  d| d  |d
  |d   d| d  |d  |d  |  d| d  |d  |d
   d| d  |d  |d   d| d  | |d  |d   d| d  |d
  |  d|  |d  | |  d|  |d
  |d   d|  |d  | |d   d|  |d  |d  |  d|  | |d   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   r   r   r      -   r   r   r   r   r   r      r   L   r   r0   r&   iX  r    r-   r+   r   r%   i  i(  r$        r,   r2      i@  r   r   r   r   r	   r
      s   n 			
		c                 C   s   | S Nr   r   r   r   r	   r
   &       c                 C   s   | | d|  S )Nr   r   r   r   r   r	   r
   '   s    c                 C   s"   | d  | d| |  |d  S )Nr   r   r   r   r   r   r	   r
   (   s   " c                 C   s   d|  | d|  S )Nr   r   r   r   r   r   r   s5r   r   r	   r
   +   r   c                 C   s   d| d  | d| d  | |  | d |d   d|  | |  d|  | |  d|d  |  d| |d   d| |  d|d   S )	Nir   r   r      r   2   (   r   r<   r   r   r	   r
   ,   s   b 

c                 C   s  d| d  | | d| d  |d   d| d  |d  |  d| d  | | |  d| d  | |  d| d  | | |  d| d  | |d   d| d  |d  |  d	| d  |d   d
|  |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   r   r   ,   B      r   r?   r*   r      r#   P   r3   r@   }        r   r<   r   r   r	   r
   .   sF   j 

c                 C   s  d| d  |d  d| d  | | |  d| d  |d  |  d| d  | |d   d| d  |d  | |  | d |d  |d   d| d  | |d   d| d  | | |  d| d  |d	   d
| d	  |d  | |  d| d	  | |d  |  d| d	  | | |d   d| d	  | |d   d| d	  |d  |  d| d  |d	  | |  d| d  |d	  |d   d	| d  |d  |d  |  d| d  |d  |d   d| d  | | | |  d| d  | |d	   d| d  |d	  |  d| d  |d  |d   d| d  | |d   d|  |d	  | |  d|  |d  |d  |  d|  |d  | |d   d|  | |d	  |  d|  | | |d   d|  | |d  |  d|  |d   d|  |d  | |  d|  | |d	   d|d  |d   d|d	  |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   r   r   r   r   r#   D   r   .   r,   r(      r"   r*      b  r6   F   )      r   r4   r   k    v    Z      r?     q  x  rG   r   r<   r   r   r	   r
   3   s   v 		
	c                 C   s  d| d  | |d  d| d  |d  |  d| d  |d  |d   d| d  | | | |  d| d  | |d   d| d  | |d   d| d  |d  | |  d	| d  | | |d   d
| d  | |d  |  d| d  |d  | |  d| d  | |d   d| d  |d   d| d  |d  |d   d| d  |d  | | |  d| d  |d  |d   d| d  | |d  |  d| d  | |d  |d   d| d  | | |d   d| d  |d  |d   d| d  | |d  |  d| d  |d   d| d  |d  | |  d| d  |d  |d  |  | d |d  | |d   d| d  |d  | |d   d| d  |d  |d  |  d| d  | |d  | |  d| d  | | |d   d| d  | |d   d| d  |d  |  d| d  |d  |d   d| d  | | |d   d| d  |d  |  d| d  |d  |d   d| d  |d  | | |  d| d  |d  |d   d| d  |d  |d  |  d | d  |d  |d  |d   d!| d  |d  | |d   d| d  | |d  |  d"| d  | |d  |d   d#| d  | | |d  |  d$| d  | |d   d%| d  |d  | |  d&| d  |d  |d   d'| d  | |d   d(| d  |d  |d   d)|  |d  | |  d*|  |d  |d  |  d|  |d  | |d   | |d  |d  |  d+|  |d  | |d   d,|  |d  |d  |  d-|  |d  |d  | |  d.|  |d  | |d   d/|  |d  |d   d0|  | |d  |  d|  | |d  |d   d1|  | | | |d   d2|  | |d  |  d|  |d  |  d3|  |d  |d   d4|  |d  |d  |  d5|  | |d   d6|  | |d   d7|d  |d   d8|d  | | |  d|d  |d   d9|d  |d  |  d|d  |d  |d   d:|d  | |d   d|d  |d  |  d;|d  |d  |d   d<|d  | |d  |  d=|d  |d   d| |d   d>| |d  | |  d$| |d  |d   d?| | |d   d@| |d  |d   dA|d  |  d|d  |d   dB|d  | |d   dC| |d  |  dD|d   dE|d   S )FNir   r   r   r   r   r    r   rT   ^   r   r   rB   r   r?   r(   >  `     r3   >  [     Y   ^  B  l     r   3   r   r,   1  <    r6      f     &     r*      n        w  p     h  R      	  l   u        E    r7   i   rX   rW   :   
  `	     5  r   r<   r   r   r	   r
   =   sJ  f 		"		





c                 C   s   d| d  |d  |d  d| d  | |d  |  | d |d   d| d  |d  | |d   d| d  |d  |d  |  d| d  | | |d   d| d  |d  |  | d	 |d  |d   d| d	  |d  | |d   d
| d	  | |d  |d   d| d	  | | |d  |  d| d	  | |d   d| d	  | |d   d| d	  |d  |d   d| d  |d  | |d   d| d  |d  |d  |  d| d  |d  |d  | |  | d |d  | |d   d| d  |d  |d   d| d  | | | |d   d| d  | |d  |  d| d  |d  |d   d| d  |d  |d  |  d| d  | |d   d| d  | |d   d| d  |d  |d   | d |d  | | |  d| d  |d  | |d   d| d  |d  |d  |d   d| d  |d  | |d  |  d| d  |d  |d   d| d  | |d  | |  d| d  | |d  |d   d| d  | | |d   d| d  | |d  |d   d| d  |d  |  d| d  |d  |d   d | d  |d  | |d   d!| d  | |d  |  d"| d  |d   d#| d  |d   d$| d  |d  | |d   d| d  |d  |d  |  d%| d  |d  |d  | |  d&| d  |d  | |d   d'| d  |d  |d   d	| d  |d  |d  |  d| d  |d  |d  |d   d(| d  |d  | | |d   d)| d  |d  |d  |  d*| d  | |d  |d   d+| 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   d| d  |d  | | |  | d |d  |d   | d |d  |d  |  d2| d  |d  | |d   d3| d  |d  |d  |d   d4| d  |d  | |d  |  d5| d  |d  |d   d6| d  |d  |d  | |  d7| d  |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  |  d@| d  |d  |d   dA| d  | | |d   dB| d  |d  |d   dC|  |d  | |d   dD|  |d  |d  |  dE|  |d  |d  | |  dF|  |d  | |d   dG|  |d  |d  |  d&|  |d  |d  |d   d&|  |d  | | |d   dH|  |d  |d  |  | |d  |d  |  dI|  |d  |d  |d   dJ|  |d  |d  |d  |  dH|  |d  | |d   dK|  |d  | |d   dL|  | |d  | |  d,|  | |d  |d   d#|  | |d  |d   dM|  | | |d  |d   dN|  | |d  |  dO|  |d	  |  d|  |d  |d   dP|  |d  | |d   dQ|  |d  |d  |  dR|  | |d   d=|  | |d   dS|  |d  |d   d1|d  |d   dT|d	  | | |  d|d	  |d   d|d  |d  |  |d |d  |d   dU|d  | |d   dV|d  |d  |d   dW|d  | |d  |  d|d  |d   d|d  |d  | |  d5|d  |d  |d   dX|d  |d  |d   d|d  |d  |  d|d  |d  |d   dY|d  |d  | |d   dZ|d  | |d  |  dR|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_|d  |d  |d   d`| |d  |  da|d	   db| |d   S )cNr-   r   r   r   r   r    r   r   r   r"   X   r   r   V   r   r   r   r>   0        r     r*   r6   r    A   r,   rP   &    ro   r   rX      +   r3   r?           v     rK       rn            r0   ]   r(   rF   b  r       r   rs      R          N   _   rA      ry   r~       r&   rw     r)          L     c             rH   N      |     @  r7   $  r   r<   r   r   r	   r
   R   s  f """				



"""""""""""     !!!!!"""
""c                 C   s    d|  | d| |  d|  S )Nr   r   r   r   r   r   r   r   r=   s6r   r   r	   r
   w   s     c                 C   s  d| d  | | d| d  |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 )Nir   r@   r   r>   r   r   r   r   r?   r      r   r   r   r   r	   r
   x   s.   b 

c                 C   s  d| d  | |d  d| d  | | |  d| d  |d   d| d  |d  |d   d| d  | | | |  d| d  | |d  |  d	| d  | | |d   d
| d  |d  | |  d| d  |d  |d   d| d  | |d  |  d| d  |d   d| d  | |d   d	| d  |d  |  d|  |d  | |  d|  |d  | | |  d|  |d  | |d   d|  |d  |d  |  d|  | |d  |  d|  | |d  | |  d|  | | |d   d|  | | |d   d|  | | | |  d|  | |d   d|  |d  | |  d|  | |d  |  d|  | | |d   d|  |d  |  d|  | |d   d|d  | |  d|d  |d   d|d  |d  |  d|d  | | |  d|d  |d   d|d  | | |  d|d  |d  |  d|d  | |d   d| |d  | |  d
| |d  |d   d| | |d  |  d| |d   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 )!NrF   r   r   rG   rH   r?   rD   r#   rE   r3   r@   rC   r   i  rA   rB   r   r*   r   i  i  r   ~   i  r-   r      r   i  rn   F    r   r   r   r   r	   r
   {   s   ^ 					





c                 C   sP  d| d  | | |d  d| d  |d  |d   d| d  | |d  |  d| d  |d   d| d  |d  | |d   d	| d  | | | |d   d
| d  | | |d  |  d| d  | |d  | |  d| d  | | |d   d| d  |d  | | |  d| d  |d  |d   d| d  | |d  |  d| d  | |d  |d   d| d  | |d   d| d  |d  |  d| d  | | |d   d| d  |d  |  d| d  |d  | |d   d| d  |d  |d  |  d| d  |d  |d  |d   d| d  |d  | | | |  d| d  |d  | |d   d| d  |d  |d  |  d| d  |d  |d  |d   d| d  |d  |d   d| d  | |d  | |  d| d  | |d  |d  |  d| d  | |d  | |d   d| d  | | |d  |  d| d  | | | |d   d| d  | |d    d!| d  | |d  |d   d"| d  | | |d  |  d| d  | |d   d#| d  |d  |d   d$| d  |d  |d  |  | d |d  |d   d%| d  |d  | |d   d&| d  |d  |d  |  d'| d  | |d  | |  d
| d  | | |d   d(| d  |d  |  d| d  |d  |d   d)| d  | |d   d*| d  |d  |d   d+|  |d  | |d   d,|  |d  | | |  d|  |d  |d   d-|  |d  |d  | |  d.|  |d  | |d  |  d|  |d  | | |d   d/|  |d  | |d   d#|  |d  |d  | |  d$|  |d  |d  |d   d|  |d  |d  |d  |  d0|  |d  | | |d   d'|  |d  | |d  |  d1|  |d  |d  | |  d|  |d  | |d   d2|  | |d  |d   d3|  | |d  | | |  d|  | |d  |d   d4|  | | |d  |  d|  | | |d  |d   d5|  | | |d   d,|  | |d  |  d6|  | | | |d   d|  | |d  |  d|  |d  | |  d|  |d  |d  |  d|  |d  | |d   d-|  |d  |d  |  d7|  |d  | |d   d|  | |d    d8|  | |d  |d   d|  | | |d  |  d|  | |d   d/|  |d  | |  d|  |d  |d   d9|  | |d   d:|d$  |d   d|d   | | |  d|d   |d  |  d|d   | |d   d|d  |d  | |  |d |d  |d   d;|d  | |d   d(|d  |d  |  d<|d  |d  |d   d4|d  | | | |  d|d  | |d   d=|d  |d  |  d|d  |d  |d   d>|d  |d   d|d  |d  | |  d|d  |d  |d  |  d|d  |d  | |d   d.|d  | |d  |  d8|d  | | |d   d|d  |d    d?|d  |d  |d   d!|d  | |d  |  d|d  |d   d@| |d  | |  d#| |d  |d  |  d| |d  |d   dA| |d  | |d   d%| |d  |d  |  d0| | |d  | |  d	| | | |d   d;| |d  |  d| |d  |d   dB| | |d   d)| |d  |d   dC|d  |d   d2|d  | | |  d<|d  |d  |  d|d  |d  |d   dD|d  |d   d+| |d  |  d5| | | |d   d| |d  |  d:|d$   d>|d  |d   d|d  |d  |  S )ENrW   r   r   rX   rY   rG   rP   r   rQ   rR   rS   rT   rU   rV   r?   r6   ie  r   i	  rK   r"   rL   rM   rN   rO   i  r   r4   r   r(   i@  r   i  iT  r*   r   i  i
  i     r   i7  r#   rI   rJ   r,   d  i	  iL  i{  ir  T   r   i(  i
    i  r-   i  rj   r   i  i  rn   i  i      r   r   r   r   r	   r
      s  f """""				


"
c                 C   s!  d| d  |d  d| d  | | |d   d| d  | | |d   d| d  | |d	  |d	   d
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|  |d	  |d   dL|  | |d  |d	   dx|  | |d  | | |  d4|  | |d  |d   dy|  | |d  |d  |  dM|  | |d  |d	  |d	   dz|  | |d  |d   dk|  | |d	  |d  |  d{|  | |d	  | | |d	   d:|  | |d	  |d  |  dI|  | | |d   d||  | | |d  |d	   dP|  | | |d	  |d	  |  d|  | | | |d   d}|  | | |d   dm|  | |d  | |  d!|  | |d  |d   d~|  | | | |d   d@|  | |d  |d	   d|  |d  | |  dT|  |d  |d	  |  dT|  |d  | |d	   dn|  |d  |d  |  d|  |d  | |d	   d	|  |d  |d   d|  |d  |d	  |d	   dV|  |d  | |d	  |  d|  |d  |d   do|  |d	  |d  | |  d#|  |d	  |d	  |d   d|  |d	  | |d   d|  | |d  |  dC|  | |d  |d	   d|  | |d	  |d   dZ|  | | |d	  |d	   d|  | |d  |  dg|  |d  |  dr|  |d  | |d	   d(|  |d	  |d  |  d|  | |d   d|  | |d   d5|dc  | |d	   dI|dc  |d	  |  dI|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	   d5|d  |d	  |d	  |  du|d  | |d	  | |  d-|d  | | |d   dI|d  |d  |d	   d|d  | |d   dd|d  |d	  |d	   d|d  |d  |d	   dy|d  |d  | | |  d6|d  |d  |d   d5|d  |d	  |d	  |d	   d|d  |d	  |d   dI|d  | |d  |  d||d  | | | |d	   d<|d  | |d  |  d|d  |d  |d	   dQ|d  |d	  |d	  |  d|d  | |d   d|d  |d   dT|d	  |d  | |  dU|d	  |d  | |d	   d	|d	  |d  |d  |  d|d	  |d  | |d	   d|d	  |d	  |d	  |d	   dW|d	  |d	  | |d	  |  d|d	  |d	  |d   dp|d	  | |d  | |  d$|d	  | |d	  |d   d|d	  | | |d   d|d	  |d  |  dD|d	  |d  |d	   d|d	  |d	  |d   d[|d	  | |d	  |d	   d|d	  |d  |  d| |d  | |d	   d]| |d  |d	  |  ds| |d  |d	  | |  d)| |d  | |d   d| |d	  |d  |  dF| |d	  |d  |d	   d| |d	  | |d   d_| |d	  |d	  |d	   dh| | |d  |  dv| | |d	  | |d	   d/| | | |d  |  d| | |d   d5| |dc   d| |d  |d	   dJ| |d  |d	  |  d| |d	  |d   d| | |d   de| |d	  |d   dL|d  | | |  d3|d  |d   d|d  |d  |  dL|d  |d	  |d	   d|d  |d   dj|d  |d  |  dz|d  | | |d	   d8|d  |d  |  dI|d	  |d   d|d	  |d  |d	   dO|d	  |d	  |d	  |  d|d	  | |d   d|d	  |d   dl| |d  | |  d | |d  |d   d}| | | |d   d>| |d  |d	   d|d  |  dB|d  |d	   d|d  |d   dS|d	  |d	  |d	   d| |d  |  d|d   d|d   S )Nir   r   rz   r   r   rX   rW   r   r   r   r   rl   rm   rs   ru   rv   rw   rx   ry   iW  r~   r   r   r7   r   r6   r   i1  it  rR   rb   rc   rd   rg   rh   ri   rj   rk   i
A  ro   rp   rq   rr   rt   ra   i*  i  iD%  i8#  r{   r|   r   r}   rf   i  r(   i  i  i
  i  i4  i  i.  i
F  r   r[   r\   r]   r^   r_   r`   r   i0  iN  re   r   r,   i  i  i`  i
  i  rn   r*   i  i  i$  i6  i  i  i c  i  iV  i  iR  rZ   i"  r   i  iؽ  i8  r    rT   r   rB   r?   i(  i 
  r3   iB  i`  iX  iz  r      r   i  i$  iz  r   i<'  i!  i   ip iXE Q   i~	  i  iF  r/   i  i/ r$   r8   i8  i  r   `  i  i @  iH	  i  D  i  i N i-  i} r   il r   r   r   r   r	   r
      sr  j """"""&&	&		"
"

""&""""""""""&&&""""&"&*""&""&"""&&""  " !!!"!""""#"##"$$$$%%%%&&&&'''"'(("(()))")*"*"*"+++,,","-&-"-.".."//"/000011"122"2333"3444455556666777788889999::::;;;;<<<<====>>>>????"@@@@AAAABBBBC"C"CDDDDEEEEFFFFGGGGHHHHIIIIIJJJJKKKKLLLLMMMMNNNNOOOO
P
Pc                 C   sXG  d| d  | |d  d| d  | | |d   d| d  | |d  |d   d| d  |d  |d   d	| d  | | | |d   d
| d  | |d  |d   d| d  |d  |d  |d   d| d  | |d  |  d| d  |d   d| d  |d   d| d  |d  | |d   d| d  |d  | | |d   d| d  |d  |d  |d   d| d  | |d  | |d   d| d  | | |d  |d   d| d  | | | |d  |d   d| d  | | |d  |  d| d  | |d  | |d   d| d  | |d  |d  |  d| d  | | |d   d| d  | | |d   d| d  |d  |d  |d   d| d  |d  |d  | |d   d| d  |d  | |d  |  d| d  |d  |d   d| d  | |d  |d   d| d  | |d  |d  |  d| d  | |d  |d   d | d  | | |d   d!| d  | |d  |d   d"| d  |d  | |  d#| d  |d  |d   d$| d  |d  | |d   d%| d  | |d  |d   d&| d  |d  |  d| d  |d  |d   d'| d  |d  | | |d   d(| d  |d  |d  |d   d)| d  |d  | |d  |d   d*| d  |d  |d  |  d| d  |d  |d  | |d   d+| d  |d  |d  |d  |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   d1| d  |d  | |d   d2| d  |d  |d  |d   d3| d  | |d  | | |d   d4| d  | |d  |d  |  d5| d  | |d  |d  |d   d6| d  | |d  |d  |d  |  d4| 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| d  | |d   d@| d  | |d   dA| d  |d  | |d   dB| d  |d  |d  |d   dC| d  |d  | |d  |  dD| d  |d  |d   dE| d  |d  |d  | |  dF| d  |d  |d  |d   dG| d  |d  | |d   dE| d  |d  |d  |  dH| d  |d  |d  |d   dI| d  |d  |d  |d   dJ| d  |d  | |d  |d   dK| d  | |d  |  dL| d  | |d  | |d   dM| d  | |d  |d  |  d| d  | | |d   dN| d  | | |d   | d |dO   dP| d  |d  |d   dQ| d  |d  |d  |  d*| d  |d  |d   dR| d  |d  |d   dS| d  | |d  |d   dT| d  |d  |d   dU| d  |d  | |d   dV| d  |d  | | |d   dW| d  |d  | |d  |d   dX| d  |d  |d  | |d   dY| d  |d  | |d  |  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  |  d9| d  |d  | | |d   d_| d  |d  | |d   dE| d  |d  |d  | |  d| d  |d  |d  |d   d`| d  |d  | | |d   da| d  |d  |d  |d   db| d  |d  |d  | |d   dc| d  |d  |d  |d  |d   dd| d  |d  |d  | |d  |  dF| d  |d  |d  |d   de| d  |d  |d  |d  | |  df| d  |d  |d  |d  |d   dg| d  |d  |d  | |d   dh| d  |d  | |d  |  d| d  |d  | |d  |d   di| d  |d  | |d  |d   dj| d  |d  | | |d  |d   dM| d  |d  | |d  |  dk| d  |d  |d  | |d   dl| d  |d  |d  |d  |  d| d  |d  | |d   dm| d  |d  | |d   dn| d  | |d  | |d   do| d  | |d  |d  |  dp| d  | |d  |d  | |  dq| d  | |d  | |d   dr| d  | |d  |d  |  d3| d  | |d  |d  |d   ds| d  | |d  | |d   dt| d  | |d  |d  |d   | d | |d  |d  |  du| d  | |d  |d  | |d   dv| d  | |d  | |d  |  d| d  | |d  |d   dw| d  | | |d  |d   dx| d  | | |d  |d  |  d-| d  | | |d  |d   dy| d  | | | |d   dz| d  | | |d  |d   dF| d  | |d  | |  dY| d  | |d  |d   d{| d  | |d  | |d   d|| d  | | |d  |d   d%| d  | |d  |  d}| d  |d  |d   d~| d  |d  | | |  d| d  |d  |d   d| d  |d  |d  |  | d |d  |d  |d   d| d  |d  |d   d| d  |d  | | |d   d| d  |d  |d  |  d| d  |d  |d  |d   d| d  |d  |d  |d  |  d4| d  |d  | |d   d| d  |d  |d   d| d  |d  |d  | |  d\| d  |d  |d  |d   d| d  |d  | | |d   d| 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   d1| |d  |d  |  d| | |d   d| | |d   d| |d  |d   d}|d  |d   d}|d  |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  | |  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   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|d  |d   d|d  |d  |d   d@| |d  |d   d|d  |  d|d   S (  Niar   r   r   r   r   r   r   r   r   r   r   r7   i  r   r   r   r   rX   rw   r   r   r   r   i  r   r   rH   rF   r   r-   iP  ibC  r   r   iO  il  i@  r   rK   r   r   r   r   r   rs   r   r   iF  i:  r3   ry   r~   r   i'  r&   r   i\  ij	  r)   i  i8'  i  iv r   r   r   r    r   r0   i}  r   rL   rE   r   i  iZ  iL r   i  i  i i  i[  r   rP   r   r   ro   r?   r   r   r   r   i-  ix(  i,  r   r   r   r   r(   i  r   i.  iB  i  i  in r   r   r   rA   r   i  i
  i  i$#  i   rW   i iq  ip?  ir$  rn   r   r   iw  i4  i  9   it  i#  iA(  i  r{   r   i`,  iV  i i`X  i i>  r   r   r>   r   r   i	  r6   r   r   r,   i  iH  i  r   r   i  im  i  i  i@V  i  r*   i  i/  i  i
  iq  i  iy i8  i!  i0 i_  i  ih  i  i-  j   i,X  i"  r   iV  iX i  i i re   r   i  ib"  r   i,     ix i i<  ih  r   i  i@ iP  r"   i  r   i  i  i  i  i  i  r1   r   i+  r2   i9  iP,  iK r   i/  i0  i   i` i r   i  i`  iܸ ip i@ ipE r   iH  r   iXD  i0 i	  i/ r   i@ r$   r   r   i   i	  i  i`K  i  i  i&  i   ir  r   i0n i i  i@  i i  r   r   r   r   r	   r
      s  n """""&"""&""				


"
"&&**&"&""&"&*"""""&""""""&"""&&""*&&*" " " "!"!&!*"*"""*#*#&#"$&$&$*%"%&%&&&&"'"'&'"("(&(")&))**&**"+&+"+,",,-"-"-....///"/0"0&011"1"2"2"2333&44455556666"7"7&7"8"8&899&9*:*:":&;&;";<"<"<&==&=&>*>&>&?*?&?*@*@&@A"A&A"BB"B"C&CC"D"D*D&E*E.E&F"F&F&G&G&GH"H"H*I"IIJ"J&J&KK&K&L"L"L&M&M*M"NN&N&OOOPP"PPQ"QQRR"RSS"ST"TT&U"UUV"V&V"WW"WXX"X"YYYYZ"ZZ[[[[\"\"\"]]]"]"^&^^_"_"_````a&a"a"b&bbcccc"d&d&de&e&e"ff"f"g&gg"h"hhi"i"i&j"j"j&k"k&k"l*l&lm"m&m"nn"noo"o"pppqq"qqr"rr"s&sst"t"t"u"uuvv&vwwwwxxxyyyyzzzz{{{"{||"|"}}}~~~~                                           "  "                  	  	  "	  	  
  "
  
  "  "                          "    "  &                    "      "  "    "  "      "  "  &      "  "                                "        "                                    !  !  !  !  "  "  "  "  #  #  #  #  $  $  $  $  %  "%  %  &  &  &  &  '  '  '  '  (  (  (  (  )  )  ) c                 C   s   | S r:   r   r   r   r   r	   r
     r;   c                 C   s   |  | ||  d|  S )Nr*   r   r   r   r   r	   r
     s    c                 C   sH   | | | d|  | |  | |d   |d |  d| |  ||  S )Nr   r   r   r   r   r   r	   r
     s   H c                 C   s   | d | | | d |d   d|  | | |  | | | |  d|  | |  |d |  d| | |  ||d   d|d  |  d| | |  |d  d|d   S )Nr   r   r*   rn   r   r   r   r   r	   r
     s   ^ 

c                 C   s0  d| d  |d  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   r   r-   r   r*   r   r   r   r   r	   r
     s.   j 
c                 C   s  | d | |d  d| d  | | |  | d |d   | d |d  |d   | d | | | |  d| d  | |d   d| d  |d  |  d|  | | |d   d|  | |d   | |d  | |  d|  | |d  |  | | | |d   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   r   r-   r   r   r   r3   rn   r   r   r   r   r	   r
     sN   j 

c                 C   s  | d | |d  d| d  | | |d   | d | |d  |  | d |d  |d   d| d  |d   d| d  | | |d   d| d  | | |d   d| d  | |d  |  d| d  |d  | |  | d | |d   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   r   r*   r>   r   r   '   r   r   r   r   r	   r
     sF   r 
c                 C   s  | d  | |d  | d | | |d   d| d  | |d   d| d  | | |d   d| d  |d  |  d| d  |d  |d   d| d  | | | |d   d| d  | |d  |d   | d | | |d  |  | d |d  | |d   d| d  | |d   d| d  |d  |d   d|  | | |d   d|  | | | |d   d|  | |d  |  d|  |d  | |d   d|  | |d  |d   d|  | | |d  |  | | |d   d	|  | |d   d|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   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
     sf   x 
c                 C   s  | d  | |d  d| d  | |d   d| d  | |d  |d   d| d  |d  |d   | d | | | |d   d| d  |d   d| d  | | |d   d| d  | | |d   d| d  | |d  |d   d| d  |d  | |d   d| d  | |d  |  d|  |d  |d  |d   d|  | |d  |d   d|  | | | | |d   | | | |d  |  | |d  | |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   r   r   r   r-   r   r   r   r   r   r   r	   r
     sV   h 
c                 C   s  | d |d  d| d  | |d   d| d  | | |d   | d |d  |d   d| d  | |d   d| d  | | |d   d| d  |d  |d   d| d  | | | |d   d| d  | | |d  |d   d| d  |d  | |d   | d |d  |d  |d   d|  | |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   r   r   r   r   r   r   r   r   r	   r
     sB   r "))r       )r      )r   r   )r   r   )r   r   N)__doc__resolvent_coeff_lambdasr   r   r   r	   <module>   sX    
M Q   /   
