from dodecanode import Node
import math
import numpy as np
import time
from scipy.sparse import csr_matrix
from scipy.sparse.linalg import eigs

def functions(n, z):
    if n == 0:
        return -1*np.conj(z)
    duals = [[], [2/(-1 + math.sqrt(5)) - 1j, 
  2/(-1 + math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/22*(-1 + 3*math.sqrt(5))*1j, 
  1/(9 + 5*math.sqrt(5))], [2/(5 *(1 + math.sqrt(5))) + 1j/math.sqrt(5), 2/(
  5 *(1 + math.sqrt(5)))], [1/22*(1 + 3*math.sqrt(5)) + 1/11*(-3 + 2*math.sqrt(5))*1j, 
  2/(13 + 5*math.sqrt(5))], [1/(2 + 2*math.sqrt(5)), 1/(
  2 + 2*math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/2*(3 - math.sqrt(5))*1j, 1/(
  7 + 3*math.sqrt(5))], [1/22*(7 - math.sqrt(5)) + 1/11*(10 - 3*math.sqrt(5))*1j, 2/(
  19 + 9*math.sqrt(5))], [2/(1 + math.sqrt(5)) + 1j, 2/(
  1 + math.sqrt(5))], [2/(11 + 5*math.sqrt(5)) + (-2 + math.sqrt(5))*1j, 2/(
  11 + 5*math.sqrt(5))], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j, 
  2/(7 + 5*math.sqrt(5))], [1/58*(11 + math.sqrt(5)) + 1/29*(-10 + 7*math.sqrt(5))*1j,
   2/(17 + 9*math.sqrt(5))]]
    return duals[n][0] + np.conj((duals[n][1])**2 / (z-duals[n][0]))

def derivatives(n, z):
    if n == 0:
        return 1
    duals = [[], [2/(-1 + math.sqrt(5)) - 1j, 
  2/(-1 + math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/22*(-1 + 3*math.sqrt(5))*1j, 
  1/(9 + 5*math.sqrt(5))], [2/(5 *(1 + math.sqrt(5))) + 1j/math.sqrt(5), 2/(
  5 *(1 + math.sqrt(5)))], [1/22*(1 + 3*math.sqrt(5)) + 1/11*(-3 + 2*math.sqrt(5))*1j, 
  2/(13 + 5*math.sqrt(5))], [1/(2 + 2*math.sqrt(5)), 1/(
  2 + 2*math.sqrt(5))], [1/4*(-1 + math.sqrt(5)) + 1/2*(3 - math.sqrt(5))*1j, 1/(
  7 + 3*math.sqrt(5))], [1/22*(7 - math.sqrt(5)) + 1/11*(10 - 3*math.sqrt(5))*1j, 2/(
  19 + 9*math.sqrt(5))], [2/(1 + math.sqrt(5)) + 1j, 2/(
  1 + math.sqrt(5))], [2/(11 + 5*math.sqrt(5)) + (-2 + math.sqrt(5))*1j, 2/(
  11 + 5*math.sqrt(5))], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j, 
  2/(7 + 5*math.sqrt(5))], [1/58*(11 + math.sqrt(5)) + 1/29*(-10 + 7*math.sqrt(5))*1j,
   2/(17 + 9*math.sqrt(5))]]
    return abs(-1*((z-duals[n][0])**2) / ((duals[n][1])**2))

def samplePoint(word):
    points = [-(1/2), 1/5 + 1/math.sqrt(5) - (2j)/5, 
1/4*(-1 + math.sqrt(5)) + 1/22*(-1 + 3*math.sqrt(5))*1j, 2/(
 5*(1 + math.sqrt(5))) + 1j/math.sqrt(5), 
1/22*(1 + 3*math.sqrt(5)) + 1/11*(-3 + 2*math.sqrt(5))*1j, 1/(2 + 2*math.sqrt(5)), 
1/4*(-1 + math.sqrt(5)) + 1/2*(3 - math.sqrt(5))*1j, 
1/22*(7 - math.sqrt(5)) + 1/11*(10 - 3*math.sqrt(5))*1j, 
2/5*(-1 + math.sqrt(5)) + (4j)/5, 2/(11 + 5*math.sqrt(5)) + (-2 + math.sqrt(5))*1j, 
1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j, 
1/58*(11 + math.sqrt(5)) + 1/29*(-10 + 7*math.sqrt(5))*1j]
    p = points[word[-1]]
    for letter in word[-2::-1]:
        p = functions(letter, p)
    return p

def sampleValue(word):
    return derivatives(word[0], samplePoint(word))

def generateTree(words, dc):
    tt = time.time()
    generators = [np.array([[0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  0, -(2/(1 + math.sqrt(5))), 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3 + math.sqrt(5), 0, 0, -1, 
  0, 0, 0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 
  1/2*(1 + math.sqrt(5)), 0, 0], [0, math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 
  0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0], [0, 
  3 + math.sqrt(5), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1 + math.sqrt(5), 0, 0, 0, 0,
   0, 0, 0], [0, 2 + math.sqrt(5), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 
  1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0], [0, 
  2 + math.sqrt(5), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0,
   0, 0, 0], [0, 1/2*(5 + math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 
  1 + math.sqrt(5), 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0], [0, 
  3 + 2*math.sqrt(5), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 
  1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 1, 0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0,
   0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 
  0, 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 
  1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 1,
   0, 0], [0, 2*(1 + math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 
  0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 2, 0, 0], [0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 1/2*(1 + 3*math.sqrt(5)),
   0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(5 - math.sqrt(5)), 0,
   0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0], [0, 1 + math.sqrt(5), 0, 0, 
  1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0, 0, 
  0, 2, 0, 0], [0, 3 + 2*math.sqrt(5), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 
  0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 2, 0, 0], [0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
  1/2*(1 - math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 1, 0, 0], [0, 1 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 
  0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0], [0, math.sqrt(5),
   0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 1/2*(5 - math.sqrt(5)), 0,
   0, 0, 0, 2, 0, 0]]), np.array([[1, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0], [1/2*(-1 - math.sqrt(5)), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0], [1/2*(-5 - 3*math.sqrt(5)), 
   1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   3/2*(3 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   0], [-(3/2)*(1 + math.sqrt(5)), 4 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-math.sqrt(5), 
   1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 + math.sqrt(5),
    0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-3 - 2*math.sqrt(5), 
   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   2*(2 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   0], [1/2*(-5 - 3*math.sqrt(5)), 2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   0], [1/2*(-7 - 3*math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0], [-3 - math.sqrt(5), 
   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0], [-2*(2 + math.sqrt(5)), 
   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   5 + 2*math.sqrt(5), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [-3 - 2*math.sqrt(5), 
   1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   5 + 2*math.sqrt(5), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   0], [1/2*(-3 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, -1, 0], [1/2*(-1 - math.sqrt(5)), 
   1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
   0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
   0], [-(3/2)*(1 + math.sqrt(5)), 3 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-math.sqrt(5), 
   3 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(3 + math.sqrt(5)),
    0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [1/2*(1 - math.sqrt(5)), 
   1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(3 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [-3 - math.sqrt(5), 
   2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 + math.sqrt(5), 
   0, 0, 0, -1, 0], [1/2*(-3 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, -1, 0]]), np.array([[0, 0, 
   0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 2*(3 + math.sqrt(5)), 7 + 3*math.sqrt(5), 
   0, 0, 0, 0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 
   0, 0, 1/2*(-3 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 5/2*(3 + math.sqrt(5)), 
   0, 0, 0, 0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 
   0, 0, -1, 1/2*(5 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 
   0, -math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)),
    2*(2 + math.sqrt(5)), 1/2*(9 + 5*math.sqrt(5)), 0, 0, 0, 0, 
   0, -5 - 2*math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 
   3 + math.sqrt(5), 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 
   1/2*(5 + math.sqrt(5)), 4 + math.sqrt(5), 0, 0, 0, 0, 0, 
   1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 
   4 + math.sqrt(5), 4 + math.sqrt(5), 0, 0, 0, 0, 0, -2*(1 + math.sqrt(5)), 0, 0, 0,
    0], [0, 0, 0, 0, 0, 0, 0, -1, 3 + math.sqrt(5), 5 + math.sqrt(5), 0, 0, 0, 
   0, 0, -2*(1 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(1 + math.sqrt(5)), 1, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 
   0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 
   1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 8 + 3*math.sqrt(5), 0, 0, 0, 
   0, 0, -3*(2 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 3 + 2*math.sqrt(5), 0, 0, 0, 0,
    0, -3 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 
   0, 0, -3 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 
   1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 7 + 3*math.sqrt(5), 0, 0, 0, 
   0, 0, -5 - 3*math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 
   1/2*(-3 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 8 + 3*math.sqrt(5), 0, 0, 0, 
   0, 0, -5 - 3*math.sqrt(5), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 2*(2 + math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 
   0, -(3/2)*(3 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 1/2*(9 + 5*math.sqrt(5)), 0, 0,
    0, 0, 0, -(3/2)*(3 + math.sqrt(5)), 0, 0, 0, 0]]), np.array([[0, 0, 0, 0, 0, -1, 
   0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 
   1/2*(5 + math.sqrt(5))], [0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0,
    0, 0, 2 + math.sqrt(5), 0, 0, 0, 0, -1, 0, 1/2*(5 + 3*math.sqrt(5))], [0, 0,
    0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 4 + math.sqrt(5), 0, 0, 
   0, 0, -1 - math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   0, 1], [0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 
   1/2*(11 + 5*math.sqrt(5))], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 
   0, 0, 0, 1 - math.sqrt(5), 0, 3 + math.sqrt(5)], [0, 0, 0, 0, 0, -1, 0, 0, 0,
    0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 
   3 + math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 0, 1/2*(1 + math.sqrt(5))], [0, 0, 0, 0, 0, 
   1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0, 
   0, 1/2*(-5 - 3*math.sqrt(5)), 0, 1/2*(13 + 5*math.sqrt(5))], [0, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0, 
   1/2*(-5 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5))], [0, 0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
    0, -3 - math.sqrt(5), 0, 2*(2 + math.sqrt(5))], [0, 0, 0, 0, 0, -1, 0, 0, 0,
    0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 
   4 + math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
   0, 0, 0], [0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, -1 - math.sqrt(5), 0, 
   2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 
   0, 0, 1 + math.sqrt(5), 0, 0, 0, 0, -1, 0, 1/2*(7 + 3*math.sqrt(5))], [0, 0, 
   0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)),
    0, 0, 0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 1/2*(13 + 5*math.sqrt(5))], [0, 0,
    0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 
   1 - math.sqrt(5), 0, 1/2*(5 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   0, 0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 
   1/2*(-5 - math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0, 0, -1, 0, 0, 0, 0, 0,
    0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 2 + math.sqrt(5), 0, 
   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1 - math.sqrt(5), 0, 0, 0, 0, 
   0, 0, -1, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 1/2*(5 + math.sqrt(5)), 0, 0, 
   0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0], [0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   1/2*(-3 - math.sqrt(5)), 0, 0, 0, 3/2*(3 + math.sqrt(5)), 0, 
   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 1, 0, 0, 0, 0], [0, 
   0, -1, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 1 + math.sqrt(5), 
   0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, -3 - math.sqrt(5), 0, 0, 0, 
   0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 
   2*(2 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0,
    0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 
   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0], [0, 
   0, 1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 3 + math.sqrt(5), 
   0, 0, 0, 0], [0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, -1, 0, 
   0, 0, 1/2*(5 + math.sqrt(5)), 0, 4 + math.sqrt(5), 0, 0, 0, 0], [0, 0, 
   1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 
   2 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0], [0, 
   0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 
   0, 0, 3/2*(3 + math.sqrt(5)), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0], [0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 
   1/2*(3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 
   1/2*(5 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0, 
   0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 
   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, -1 - math.sqrt(5), 0, 0, 0, 0, 
   0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 
   2*(3 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0,
    0, 0, 0, -1, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0, 
   0], [0, 0, -1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 
   0, 0, 4 + math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0]]), np.array([[0, 0, 
   0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 4 + math.sqrt(5), 0,
    0, 0, 1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 
   0, 0, 0, 1, 0], [0, 0, 0, 0, -1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 
   3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 0], [0,
    0, 0, 0, 1/2*(-7 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0,
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 
   1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)),
    0, 0, 0, 1/2*(-1 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 0], [0, 0, 0, 
   0, -1 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 
   0, 1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 0, 
   1/2*(-9 - 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)),
    0, 0, 0, 1/2*(-1 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0], [0, 0, 0, 
   0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 
   0, 0, 0, 1/2*(1 - math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 0], [0, 0, 0, 
   0, -2*(2 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 
   0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2*(3 + math.sqrt(5)), 0], [0, 0, 0, 
   0, -2 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0,
    0, -1, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 0, 0, 0, -2*(2 + math.sqrt(5)), 0, 
   0, 0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   1/2*(11 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0, 
   0, 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 
   4 + math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
   0, 0, 0, 0], [0, 0, 0, 0, 1/2*(-7 - 3*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, -1, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 0,
    0, 0, -2 - math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 
   0, 0, 0, -1, 1/2*(5 + 3*math.sqrt(5)), 0], [0, 0, 0, 0, 
   1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
   1/2*(1 + math.sqrt(5)), 0], [0, 0, 0, 0, -2*(2 + math.sqrt(5)), 0, 0, 0, 0, 
   0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, -1, 2*(2 + math.sqrt(5)), 0], [0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0,
    0, 1/2*(-11 - 5*math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   1/2*(13 + 5*math.sqrt(5)), 0]]), np.array([[0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 
   1 + math.sqrt(5), 0, 1 + math.sqrt(5), 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 1/2*(5 + math.sqrt(5)), 0, 3 + math.sqrt(5),
    0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 
   1/2*(1 - math.sqrt(5)), math.sqrt(5), 0, 1/2*(3 + math.sqrt(5)), 0, 1 + math.sqrt(5), 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 
   3 - math.sqrt(5), 0, 1 + math.sqrt(5), 0, 1/2*(5 - math.sqrt(5)), 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 2, 0, 3 + math.sqrt(5), 0, 3 + math.sqrt(5),
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 
   1/2*(-1 + math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 1 + math.sqrt(5), 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0], [0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 1/2*(-1 + math.sqrt(5)), 0, 
   1 + math.sqrt(5), 0, 2 + math.sqrt(5), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 
   0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0,
    1/2*(-3 + math.sqrt(5)), 2 - math.sqrt(5), 0, 1/2*(3 + math.sqrt(5)), 0, 3, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 
   1/2*(-1 + math.sqrt(5)), 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 
   0, 1/2*(1 - math.sqrt(5)), math.sqrt(5), 0, 2 + math.sqrt(5), 0, 
   1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 
   3, 0, 3/2*(1 + math.sqrt(5)), 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 1/2*(7 - math.sqrt(5)), 0, 
   1/2*(1 + math.sqrt(5)), 0, 1/2*(5 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 3 - math.sqrt(5), 0, 
   1/2*(1 + math.sqrt(5)), 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 
   0, -1, 3, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 
   1/2*(7 - math.sqrt(5)), 0, 1/2*(3 + math.sqrt(5)), 0, 1/2*(3 - math.sqrt(5)), 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 2, 0, 
   1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0], [0, 0, 0, 0, 0, 1, 0, 1/2*(-1 + math.sqrt(5)), 0, 
   1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]), np.array([[0, 0, 0, 1, 0,
    0, 4 + math.sqrt(5), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 
   1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 
   1/2*(7 + 3*math.sqrt(5)), 4 + math.sqrt(5), 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 
   0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 
   3/2*(3 + math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 
   1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 
   1/2*(5 + 3*math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
   0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 2 + math.sqrt(5), 
   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0,
    0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0], [0, 0, 0, -math.sqrt(5), 0, 0, 1/2*(7 + math.sqrt(5)), 1/2*(5 + math.sqrt(5)),
    0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -math.sqrt(5), 0, 0, 
   1/2*(5 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, -1, 0, 0, 0, 0, 
   0, 0, 0], [0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 1/2*(1 + math.sqrt(5)), 1,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1/2*(-1 - math.sqrt(5)),
    0, 0, 1, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0], [0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 
   0], [0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 3/2*(3 + math.sqrt(5)), 
   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0,
    0, 0], [0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 
   3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 0, 0, 0, 
   0, 0], [0, 0, 0, 1/2*(-3 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 
   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0,
    0, 0], [0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 
   1 + math.sqrt(5), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   0], [0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 1 + math.sqrt(5), 2 + math.sqrt(5), 0,
    0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 
   1/2*(3 - math.sqrt(5)), 0, 0, 1/2*(5 + math.sqrt(5)), 2, 0, 0, 0, 0, -1, 0, 
   0, 0, 0, 0, 0, 0], [0, 0, 0, 1/2*(3 - math.sqrt(5)), 0, 0, 2, 
   1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0]]), np.array([[0, 0, 
   0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
   1/2*(-1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 1/2*(7 - 3*math.sqrt(5)), 0, 
   0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 5 - math.sqrt(5), 0, 0, 
   2*(-1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, -(3/2)*(-3 + math.sqrt(5)), 0, 
   0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 5 - math.sqrt(5), 0, 
   0, -3 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 1/2*(-1 + 3*math.sqrt(5)), 0, 
   0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, -1 + math.sqrt(5), 0, 0, 4, 0, 
   0], [0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 
   0, 0, 3/2*(1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 0, 
   0, 0, 3, 0, 0, 1 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 5 - math.sqrt(5), 
   0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(7 - 3*math.sqrt(5)), 0, 0,
    2*(-1 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 0, 0, 
   0, 4, 0, 0, 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 5 - math.sqrt(5), 0, 0, 
   1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, -(3/2)*(-3 + math.sqrt(5)), 0, 
   0, -3 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 
   0, -1, 0, 0, 0, 0, 0, 3, 0, 0, 3/2*(1 + math.sqrt(5)), 0, 0], [0, 0, 0, 
   0, 0, 1/2*(1 + 3*math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 
   0, -1 + math.sqrt(5), 0, 0, 3, 0, 0], [0, 0, 0, 0, 
   0, -(3/2)*(-3 + math.sqrt(5)), 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 
   0, -(3/2)*(-3 + math.sqrt(5)), 0, 0, 5/2*(-1 + math.sqrt(5)), 0, 0], [0, 0, 
   0, 0, 0, -1 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(1 + 3*math.sqrt(5)), 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 
   1/2*(-1 + 3*math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(-1 + 3*math.sqrt(5)), 0, 0, 1/2*(7 - math.sqrt(5)), 0, 0], [0, 0, 0, 0, 
   0, -1 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(-1 + 3*math.sqrt(5)), 0, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 
   0, 0, 0, 0, 4, 0, 0, 1 + 2*math.sqrt(5), 0, 0], [0, 0, 0, 0, 0, 1, 0, 0,
    0, 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(-1 + math.sqrt(5)), 0, 
   0]]), np.array([[0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1 + math.sqrt(5), 0, -1 + math.sqrt(5), 
   0], [0, 0, 0, 3/2*(-1 + math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(7 - math.sqrt(5)), 
   0, -(3/2)*(-3 + math.sqrt(5)), 0], [0, 0, 0, 1 + 2*math.sqrt(5), 0, 0, 0, 0, 
   0, -1, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 3/2*(-1 + math.sqrt(5)), 0, 
   0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 3 - math.sqrt(5), 0, 
   5 - math.sqrt(5), 0], [0, 0, 0, 2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, -1, 0, 
   0, 0, 0, 0, 0, 3, 0, 3, 0], [0, 0, 0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, -(2/(1 + math.sqrt(5))), 0, 1, 0], [0, 0, 
   0, -1 + 2*math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 
   0, 0, 3 - math.sqrt(5), 0, -(3/2)*(-3 + math.sqrt(5)), 0], [0, 0, 0, 
   1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0,
    0, 1/2*(-1 + math.sqrt(5)), 0, 1/2*(1 + 3*math.sqrt(5)), 0], [0, 0, 0, 
   2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 4, 
   0], [0, 0, 0, 1/2*(-1 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 2 - math.sqrt(5), 0, 5 - math.sqrt(5), 
   0], [0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 
   0, 0, 0, 0, 0, 0, 1/2*(-1 + math.sqrt(5)), 0, 1/2*(-1 + 3*math.sqrt(5)), 
   0], [0, 0, 0, 2/(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   1, 0, 1/2*(1 - math.sqrt(5)), 0], [0, 0, 0, 3, 0, 0, 0, 0, 0, 
   1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, math.sqrt(5), 0, 
   1/2*(-1 + 3*math.sqrt(5)), 0], [0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 
   0, 0, -1, 0, 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 3, 0], [0, 0, 0, 
   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 
   1/2*(7 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 1, 0, 0, 0], [0, 0, 0, 1/2*(-1 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(-3 + math.sqrt(5)), 0, 0, 0, 0, 0, 0, 1/2*(7 - math.sqrt(5)), 0, 
   1/2*(7 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 1, 0], [0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0, 0, 
   1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, math.sqrt(5), 0, -1 + math.sqrt(5), 
   0]]), np.array([[0, 0, 5, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0,
   0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 2*(1 + math.sqrt(5)), 0, 0,
   0, 1/2*(1 - math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0, 
  1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0, -1, 
  0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0, 
  0], [0, 0, 3/2*(1 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 
  2 + math.sqrt(5), 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 
  0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0,
   0], [0, 0, 5 + math.sqrt(5), 0, 0, 0, -1, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 
  0, 0, 0, -1 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 3/2*(1 + math.sqrt(5)), 0, 0, 
  0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 
  1/2*(-5 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 1/2*(7 - math.sqrt(5)), 0, 0, 0, 
  1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 
  1/2*(3 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1/2*(1 + 3*math.sqrt(5)), 0, 0, 0, 
  1/2*(1 - math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0, -1, 0, 0, 0, 
  0], [0, 0, 1/2*(7 - math.sqrt(5)), 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 
  2 + math.sqrt(5), 0, 0, 0, 0, 0, 1 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 
  1/2*(11 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 
  0, 1/2*(-5 - 3*math.sqrt(5)), 0, 0, 0, 0], [0, 0, 4, 0, 0, 0, 
  1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 
  1 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 1/2*(1 + math.sqrt(5)), 0, 0, 0, 0, 0, 
  0, 1, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0], [0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 
  1/2*(11 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 
  0, 0, -(3/2)*(1 + math.sqrt(5)), 0, 0, 0, 0], [0, 0, 2*(1 + math.sqrt(5)), 0, 
  0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 
  0, -3 - math.sqrt(5), 0, 0, 0, 0], [0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0, -1,
   0, 0, 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, -1 - math.sqrt(5), 0, 0, 0, 
  0], [0, 0, 4, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0, 0, 
  0, 0, 0, 1/2*(-1 - 3*math.sqrt(5)), 0, 0, 0, 0]]), np.array([[0, 0, 0, 0, 
   1/2*(11 + 5*math.sqrt(5)), 0, 2*(3 + math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)),
    0, 0, 0, 0, 0, 0, 0, 0, -2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 
   1/2*(7 + 3*math.sqrt(5)), 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 
   0, 0, 0, 0, -2 - math.sqrt(5), 0], [0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0, 
   1/2*(7 + 3*math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(-7 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 
   3 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 
   0, -1 - math.sqrt(5), 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
   0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 
   1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   0, 0, 1/2*(-11 - 5*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 
   2*(2 + math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(-7 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(1 + math.sqrt(5)), 0, 1, 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [0, 0, 0, 0, 
   2*(2 + math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 0, 0, 0,
    0, -2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 1, 0, 1/2*(1 + math.sqrt(5)), 0, 
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [0, 0, 0, 0, 
   3 + math.sqrt(5), 0, 4 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 
   0, 0, 0, 0, 1/2*(-5 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 
   1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, -1, 0, 0, 0, 0, 
   0, 0, 0, 0, -2 - math.sqrt(5), 0], [0, 0, 0, 0, 3 + math.sqrt(5), 0, 
   1/2*(5 + math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 
   0, -1 - math.sqrt(5), 0], [0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 
   1/2*(11 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0], [0, 0, 0, 0, 4 + math.sqrt(5), 0, 
   3 + math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0, 
   1/2*(-5 - 3*math.sqrt(5)), 0], [0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 
   1/2*(5 + math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 0, 0,
    1/2*(-1 - math.sqrt(5)), 0], [0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 
   1/2*(11 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   0, 0, -2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 
   1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 0, 0, 0, 0, 
   0, 0, 1/2*(-9 - 5*math.sqrt(5)), 0]])]

    root = Node([-1, 2, 1/2*(11 + 5*math.sqrt(5)), 1/2*(23 + 9*math.sqrt(5)), 3/2*(7 + 
   3*math.sqrt(5)), 3*(2 + math.sqrt(5)), 1/2*(27 + 13*math.sqrt(5)), 12 + 
 5*math.sqrt(5), 1/2*(29 + 13*math.sqrt(5)), 13 + 5*math.sqrt(5), 18 + 
 7*math.sqrt(5), 15 + 7*math.sqrt(5), 5 + 2*math.sqrt(5), 5 + 
 2*math.sqrt(5), 1/2*(7 + math.sqrt(5)), 12 + 
 5*math.sqrt(5), 2*(2 + math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 11 + 
 4*math.sqrt(5), 1/2*(13 + 5*math.sqrt(5))], [], words, False)

    #print(root.tuple)
    #print(np.matmul(generators[0],root.tuple))
    current_leaves = [root]
    nodes = 1
    while True:
        new_leaves = []
        for leaf in current_leaves:
            next_gen = leaf.next_generation(words, dc, generators)
            new_leaves += next_gen
            nodes += len(next_gen) if len(next_gen) > 1 else 0
        if current_leaves == new_leaves:
            break
        else:
            current_leaves = new_leaves
    for i,leaf in enumerate(current_leaves):
        words[str(leaf.word)] = i
    print(len(current_leaves), "partitions")
    print(nodes,"nodes")
    print("tree construction (s): %f\ntree construction (m): %f" % (time.time()-tt, (time.time()-tt)/60))
    return current_leaves

def constructMatrix(words, dc):
    leave = generateTree(words, dc)
    row = []
    col = []
    data = []
    for i,leaf in enumerate(leave):
        print(leaf.word)
        thing = words[str(leaf.word[1:])]
        if isinstance(thing,int):
            row.append(i)
            col.append(thing)
            data.append(sampleValue(leaf.word))
        else:
            sample = sampleValue(leaf.word)
            for wor in thing.leaves():
                row.append(i)
                col.append(words[str(wor.word)])
                data.append(sample)
    return csr_matrix((data,(row,col)),shape=(len(leave),len(leave)))

def secant(x0,y0,x1,y1,z):
    return x0 - (y0-z) * ((x1-x0)/(y1-y0))

def matrixFunction(matrix,l,a):
    #return np.real(eigs(matrix.power(a),k=1)[0][0])
    matrix = matrix.power(a)
    vec = np.ones(l)
    previous_entry = vec[0]
    previous_val = 0
    current = matrix * vec
    current_val = current[0] / previous_entry
    count = 0
    while count < 10000000000 and abs(current_val - previous_val) > 1e-10:
        previous_val = current_val
        previous_entry = current[0]
        current = matrix * current
        #print(current[0],previous_entry)
        current_val = current[0] / previous_entry
        count += 1
    print("power method:", count)
    return current_val

def secantMethod(matrix,l,z,x1,x2,e,its):
    k1 = x1
    k2 = x2
    y1 = matrixFunction(matrix,l,k1)
    y2 = matrixFunction(matrix,l,k2)
    #y1 = testFunction(k1)
    #y2 = testFunction(k2)
    count = 1
    print(count,k1,y1)
    while abs(y1-z)>e and count<its:
        k3 = secant(k1,y1,k2,y2,z)
        k1 = k2
        y1 = y2
        k2 = k3
        y2 = matrixFunction(matrix,l,k2)
        #y2 = testFunction(k2)
        count += 1
        print(count,k1,y1)

def main():
    start = time.time()

    words = {}
    m = 600
    print("maximum:",m)
    matrix = constructMatrix(words, m)
    #print(matrix)
    
    print("construction (s): %f\nconstruction (m): %f" % (time.time()-start, (time.time()-start)/60))
    #print(csr_matrix.transpose(matrix))
    print(csr_matrix.count_nonzero(matrix), (matrix.shape[0])*11)
    secantMethod(matrix,matrix.shape[0],1,1.55,1.59,10**(-10),1000)

    print("total (s): %f\ntotal (m): %f" % (time.time()-start, (time.time()-start)/60))

main()