From dc79323588c0f7da9984b218338db84aa56c7787 Mon Sep 17 00:00:00 2001
From: EmmiRiv <73808999+EmmiRiv@users.noreply.github.com>
Date: Tue, 3 Aug 2021 15:08:06 -0500
Subject: [PATCH] Add files via upload

---
 .../mcmullen_stuff/dodecanode.py              |  84 +++
 .../mcmullen_stuff/dodecatree.py              | 563 ++++++++++++++++++
 fractal_dimension/mcmullen_stuff/icosanode.py |  84 +++
 fractal_dimension/mcmullen_stuff/icosatree.py | 492 +++++++++++++++
 4 files changed, 1223 insertions(+)
 create mode 100644 fractal_dimension/mcmullen_stuff/dodecanode.py
 create mode 100644 fractal_dimension/mcmullen_stuff/dodecatree.py
 create mode 100644 fractal_dimension/mcmullen_stuff/icosanode.py
 create mode 100644 fractal_dimension/mcmullen_stuff/icosatree.py

diff --git a/fractal_dimension/mcmullen_stuff/dodecanode.py b/fractal_dimension/mcmullen_stuff/dodecanode.py
new file mode 100644
index 0000000..2fce236
--- /dev/null
+++ b/fractal_dimension/mcmullen_stuff/dodecanode.py
@@ -0,0 +1,84 @@
+import numpy as np
+import math
+from random import sample
+
+class Node:
+    def __init__(self, tuple, word, words, infertile):
+        self.tuple = tuple
+        self.children = []
+        self.word = word
+        self.infertile = infertile
+        words[str(word)] = self
+
+    def dc_not_too_big(self, g, generator, dual_curvature):
+        temp = np.matmul(generator, self.tuple)
+        if g == 0:
+            temp = [temp[i] for i in (0,1,16,12,17)]
+        elif g == 1:
+            temp = [temp[i] for i in (0,1,13,12,14)]
+        elif g == 2:
+            temp = [temp[i] for i in (9,11,19,8,15)]
+        elif g == 3:
+            temp = [temp[i] for i in (3,7,19,17,12)]
+        elif g == 4:
+            temp = [temp[i] for i in (2,13,4,8,15)]
+        elif g == 5:
+            temp = [temp[i] for i in (4,13,1,16,18)]
+        elif g == 6:
+            temp = [temp[i] for i in (7,11,9,5,19)]
+        elif g == 7:
+            temp = [temp[i] for i in (3,7,11,10,6)]
+        elif g == 8:
+            temp = [temp[i] for i in (0,14,5,19,17)]
+        elif g == 9:
+            temp = [temp[i] for i in (3,6,18,16,12)]
+        elif g == 10:
+            temp = [temp[i] for i in (2,14,5,9,15)]
+        elif g == 11:
+            temp = [temp[i] for i in (4,8,10,6,18)]
+        if temp[0] < 0:
+            return math.sqrt(-((temp[0]*temp[1]*temp[2] + temp[0]*temp[1]*temp[3] + temp[0]*temp[2]*temp[3] - temp[1]*temp[2]*temp[3] + temp[0]*temp[1]*temp[4] + 
+  temp[0]*temp[2]*temp[4] - temp[1]*temp[2]*temp[4] + temp[0]*temp[3]*temp[4] - temp[1]*temp[3]*temp[4] - temp[2]*temp[3]*temp[4] - 
+  math.sqrt(-4*temp[0]*temp[1]*temp[2]*temp[3]*(temp[0] - temp[1] - temp[2] - temp[3] - temp[4])*temp[4] + (temp[2]*temp[3]*temp[4] + 
+     temp[1]*(temp[3]*temp[4] + temp[2]*(temp[3] + temp[4])) - 
+     temp[0]*(temp[3]*temp[4] + temp[2]*(temp[3] + temp[4]) + temp[1]*(temp[2] + temp[3] + temp[4])))**2))/(-temp[0] + temp[1] + 
+  temp[2] + temp[3] + temp[4])))/math.sqrt(2) < dual_curvature
+        else:
+            return (1/math.sqrt(2))*(math.sqrt(temp[0]*temp[1] + temp[0]*temp[2] + temp[1]*temp[2] + temp[0]*temp[3] + temp[1]*temp[3] + temp[2]*temp[3] + 
+    temp[0]*temp[4] + temp[1]*temp[4] + temp[2]*temp[4] + temp[3]*temp[4] - 
+    math.sqrt(-4*temp[0]*temp[1]*temp[2]*temp[3] - 4*temp[0]*temp[1]*temp[2]*temp[4] - 4*temp[0]*temp[1]*temp[3]*temp[4] - 
+     4*temp[0]*temp[2]*temp[3]*temp[4] - 
+     4*temp[1]*temp[2]*temp[3]*temp[4] + (temp[2]*temp[3] + temp[2]*temp[4] + temp[3]*temp[4] + temp[1]*(temp[2] + temp[3] + temp[4]) + 
+       temp[0]*(temp[1] + temp[2] + temp[3] + temp[4]))**2))) < dual_curvature
+
+    def next_generation(self, words, dual_curvature, generators):
+        if self.infertile:
+            return [self]
+        if self.children == []:
+            for g,generator in enumerate(generators):
+                if len(self.word) == 0 or g != self.word[-1]:
+                    if self.word + [g] == [1, 8, 15, 8, 0] or self.word + [g] == [8, 15, 8, 0]:
+                        print(self.tuple)
+                    self.children.append(Node(np.matmul(generator,self.tuple), self.word[:] + [g], words, not self.dc_not_too_big(g, generator, dual_curvature)))
+        if self.children == []:
+            return [self]
+        else:
+            return self.children
+    
+    def next(self):
+        if self.children == []:
+            return [self]
+        else:
+            return self.children
+    
+    def leaves(self):
+        current_leaves = [self]
+        while True:
+            new_leaves = []
+            for leaf in current_leaves:
+                new_leaves += leaf.next()
+            if current_leaves == new_leaves:
+                break
+            else:
+                current_leaves = new_leaves
+        return current_leaves
\ No newline at end of file
diff --git a/fractal_dimension/mcmullen_stuff/dodecatree.py b/fractal_dimension/mcmullen_stuff/dodecatree.py
new file mode 100644
index 0000000..0b8e102
--- /dev/null
+++ b/fractal_dimension/mcmullen_stuff/dodecatree.py
@@ -0,0 +1,563 @@
+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,
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+   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0, 0, -1, 0, 0, 0, 0, 0,
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+   0, 0, 4 + math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0]]), np.array([[0, 0, 
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+   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)), 
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+   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()
\ No newline at end of file
diff --git a/fractal_dimension/mcmullen_stuff/icosanode.py b/fractal_dimension/mcmullen_stuff/icosanode.py
new file mode 100644
index 0000000..438fff2
--- /dev/null
+++ b/fractal_dimension/mcmullen_stuff/icosanode.py
@@ -0,0 +1,84 @@
+import numpy as np
+import math
+
+class Node:
+    def __init__(self, tuple, word, words, infertile):
+        self.tuple = tuple
+        self.children = []
+        self.word = word
+        self.infertile = infertile
+        words[str(word)] = self
+
+    def dc_not_too_big(self, g, generator, dual_curvature):
+        temp = np.matmul(generator, self.tuple)
+        if g == 0:
+            temp = [temp[i] for i in (0,1,8)]
+        elif g == 1:
+            temp = [temp[i] for i in (0,1,5)]
+        elif g == 2:
+            temp = [temp[i] for i in (1,4,10)]
+        elif g == 3:
+            temp = [temp[i] for i in (3,7,9)]
+        elif g == 4:
+            temp = [temp[i] for i in (4,5,11)]
+        elif g == 5:
+            temp = [temp[i] for i in (6,8,10)]
+        elif g == 6:
+            temp = [temp[i] for i in (7,9,11)]
+        elif g == 7:
+            temp = [temp[i] for i in (3,6,7)]
+        elif g == 8:
+            temp = [temp[i] for i in (2,4,11)]
+        elif g == 9:
+            temp = [temp[i] for i in (2,6,10)]
+        elif g == 10:
+            temp = [temp[i] for i in (2,7,11)]
+        elif g == 11:
+            temp = [temp[i] for i in (2,6,7)]
+        elif g == 12:
+            temp = [temp[i] for i in (0,3,9)]
+        elif g == 13:
+            temp = [temp[i] for i in (1,4,5)]
+        elif g == 14:
+            temp = [temp[i] for i in (1,8,10)]
+        elif g == 15:
+            temp = [temp[i] for i in (2,4,10)]
+        elif g == 16:
+            temp = [temp[i] for i in (0,5,9)]
+        elif g == 17:
+            temp = [temp[i] for i in (0,3,8)]
+        elif g == 18:
+            temp = [temp[i] for i in (5,9,11)]
+        elif g == 19:
+            temp = [temp[i] for i in (3,6,8)]
+        return math.sqrt(temp[0]*temp[1] + temp[0]*temp[2] + temp[1]*temp[2]) < dual_curvature
+    
+    def next_generation(self, words, dual_curvature, generators):
+        if self.infertile:
+            return [self]
+        if self.children == []:
+            for g,generator in enumerate(generators):
+                if len(self.word) == 0 or g != self.word[-1]:
+                    self.children.append(Node(np.matmul(generator,self.tuple), self.word[:] + [g], words, not self.dc_not_too_big(g, generator, dual_curvature)))
+        if self.children == []:
+            return [self]
+        else:
+            return self.children
+    
+    def next(self):
+        if self.children == []:
+            return [self]
+        else:
+            return self.children
+    
+    def leaves(self):
+        current_leaves = [self]
+        while True:
+            new_leaves = []
+            for leaf in current_leaves:
+                new_leaves += leaf.next()
+            if current_leaves == new_leaves:
+                break
+            else:
+                current_leaves = new_leaves
+        return current_leaves
\ No newline at end of file
diff --git a/fractal_dimension/mcmullen_stuff/icosatree.py b/fractal_dimension/mcmullen_stuff/icosatree.py
new file mode 100644
index 0000000..4a6cbbd
--- /dev/null
+++ b/fractal_dimension/mcmullen_stuff/icosatree.py
@@ -0,0 +1,492 @@
+from icosanode 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 == 1:
+        return -1*np.conj(z)
+    duals = [[1/2*(-1 + math.sqrt(5)) - 1j, 1/2*(-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))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(6 - math.sqrt(5))*1j, 
+  2/(11 + 7*math.sqrt(5))], [1/22*(1 + 3*math.sqrt(5)) + 
+   1/11*(-3 + 2*math.sqrt(5))*1j, 2/(
+  13 + 5*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(-4 + math.sqrt(5))*1j, 2/(
+  17 + 7*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(4 - math.sqrt(5))*1j, 2/(
+  17 + 7*math.sqrt(5))], [3/(2*math.sqrt(5)), 1/(
+  10 + 4*math.sqrt(5))], [1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(2/5) + 1/
+   math.sqrt(5)], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(-8 + 3*math.sqrt(5))*1j, 2/(
+  23 + 11*math.sqrt(5))], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(8 - 3*math.sqrt(5))*1j,
+   2/(23 + 11*math.sqrt(5))], [1/6*(-1 + 2*math.sqrt(5)), 
+  1/6*(-2 + math.sqrt(5))], [1 + (-2 + math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/(
+  2 + 2*math.sqrt(5)), 1/(
+  2 + 2*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/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, -(2/5) + 1/
+   math.sqrt(5)], [2/(1 + math.sqrt(5)) + 1j, 2/(
+  1 + math.sqrt(5))], [1 + (2 - math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j, 2/(
+  7 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(-6 + math.sqrt(5))*1j, 
+  2/(11 + 7*math.sqrt(5))]]
+    return duals[n][0] + np.conj((duals[n][1])**2 / (z-duals[n][0]))
+
+def derivatives(n, z):
+    if n == 1:
+        return 1
+    duals = [[1/2*(-1 + math.sqrt(5)) - 1j, 1/2*(-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))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(6 - math.sqrt(5))*1j, 
+  2/(11 + 7*math.sqrt(5))], [1/22*(1 + 3*math.sqrt(5)) + 
+   1/11*(-3 + 2*math.sqrt(5))*1j, 2/(
+  13 + 5*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(-4 + math.sqrt(5))*1j, 2/(
+  17 + 7*math.sqrt(5))], [1/22*(15 - math.sqrt(5)) + 1/11*(4 - math.sqrt(5))*1j, 2/(
+  17 + 7*math.sqrt(5))], [3/(2*math.sqrt(5)), 1/(
+  10 + 4*math.sqrt(5))], [1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(2/5) + 1/
+   math.sqrt(5)], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(-8 + 3*math.sqrt(5))*1j, 2/(
+  23 + 11*math.sqrt(5))], [-(3/38)*(-9 + math.sqrt(5)) + 1/19*(8 - 3*math.sqrt(5))*1j,
+   2/(23 + 11*math.sqrt(5))], [1/6*(-1 + 2*math.sqrt(5)), 
+  1/6*(-2 + math.sqrt(5))], [1 + (-2 + math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/(
+  2 + 2*math.sqrt(5)), 1/(
+  2 + 2*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/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, -(2/5) + 1/
+   math.sqrt(5)], [2/(1 + math.sqrt(5)) + 1j, 2/(
+  1 + math.sqrt(5))], [1 + (2 - math.sqrt(5))*1j, -2 + math.sqrt(5)], [1/38*(11 + 3*math.sqrt(5)) + 1/19*(1 + 2*math.sqrt(5))*1j, 2/(
+  7 + 5*math.sqrt(5))], [1/62*(15 + 13*math.sqrt(5)) + 1/31*(-6 + math.sqrt(5))*1j, 
+  2/(11 + 7*math.sqrt(5))]]
+    return abs(-1*((z-duals[n][0])**2) / ((duals[n][1])**2))
+
+def samplePoint(word):
+    points = [2/5*(-1 + math.sqrt(5)) - (4j)/5, -(1/
+   2), 1/22*(1 + 3*math.sqrt(5)) + (1/100 + 1/11*(3 - 2*math.sqrt(5)))*1j, 1/
+    62*(15 + 13*math.sqrt(5)) + 
+   1/31*(6 - math.sqrt(5))*1j, 1/
+    22*(1 + 3*math.sqrt(5)) + (-(1/100) + 1/11*(-3 + 2*math.sqrt(5)))*1j, 1/
+    22*(15 - math.sqrt(5)) + 
+   1/11*(-4 + math.sqrt(5))*1j, 1/22*(15 - math.sqrt(5)) + 
+   1/11*(4 - math.sqrt(5))*1j, 3/(
+  2*math.sqrt(5)), 1/math.sqrt(5) + (-(2/5) + 1/math.sqrt(5))*1j, -(3/38)*(-9 + math.sqrt(5)) + 
+   1/19*(-8 + 3*math.sqrt(5))*1j, -(3/38)*(-9 + math.sqrt(5)) + 
+   1/19*(8 - 3*math.sqrt(5))*1j, 1/6*(-1 + 2*math.sqrt(5)), 9/10 + 
+   9/10*(-2 + math.sqrt(5))*1j, 1/(
+  2 + 2*math.sqrt(5)), 1/38*(11 + 3*math.sqrt(5)) + 
+   1/19*(-1 - 2*math.sqrt(5))*1j, 1/math.sqrt(5) + (2/5 - 1/math.sqrt(5))*1j, 8/(
+   5*(1 + math.sqrt(5))) + (4j)/5, 9/10 + 
+   9/10*(2 - math.sqrt(5))*1j, 1/38*(11 + 3*math.sqrt(5)) + 
+   1/19*(1 + 2*math.sqrt(5))*1j, 1/62*(15 + 13*math.sqrt(5)) + 
+   1/31*(-6 + 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([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0], [5 + 2*math.sqrt(5), 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, -1, 
+   2*(3 + math.sqrt(5)), 0, 0, 0], [1/2*(7 + math.sqrt(5)), 1/2*(3 + math.sqrt(5)), 
+   0, 0, 0, 0, 0, 1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 
+   0], [1/2*(5 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 
+   1/2*(1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 
+   0], [1/2*(7 + math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0, 
+   1/2*(-3 + math.sqrt(5)), 3, 0, 0, 0], [1/2*(5 + 3*math.sqrt(5)), 3 + math.sqrt(5),
+    0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 3 + 2*math.sqrt(5), 0, 0, 
+   0], [2*(3 + math.sqrt(5)), 2*(2 + 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, 1, 0, 0, 
+   0], [3 + 2*math.sqrt(5), 3 + math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 
+   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0], [3, 2 + math.sqrt(5), 0, 0, 0, 0, 0, 
+   1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0], [2*(3 + math.sqrt(5)), 
+   5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, -1, 5 + 2*math.sqrt(5), 0, 0, 0]]), np.array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
+  0, 0], [2*(2 + math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 
+  5 + 2*math.sqrt(5), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
+  0], [1/2*(7 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 3 + math.sqrt(5),
+   0, 0, 0, 0, -1, 0], [1/2*(3 + math.sqrt(5)), 3 + math.sqrt(5), 0, 0, 0, 
+  2 + math.sqrt(5), 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [0, 0, 0, 0, 0, 1, 
+  0, 0, 0, 0, 0, 0], [5 + 2*math.sqrt(5), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 
+  2*(2 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0], [5 + 2*math.sqrt(5),
+   1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 
+  1/2*(-1 - math.sqrt(5)), 0], [2 + math.sqrt(5), 3 + math.sqrt(5), 0, 0, 0, 
+  1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0], [2 + math.sqrt(5), 
+  1/2*(5 + math.sqrt(5)), 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0, 
+  1/2*(1 - math.sqrt(5)), 0], [3 + math.sqrt(5), 2*(2 + math.sqrt(5)), 0, 0, 0, 
+  3 + math.sqrt(5), 0, 0, 0, 0, -1, 0], [3 + math.sqrt(5), 1/2*(7 + 3*math.sqrt(5)), 
+  0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, -1, 0]]), np.array([[0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 
+   1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0], [0, 1, 0, 0, 0, 
+   0, 0, 0, 0, 0, 0, 0], [0, 1/2*(3 + math.sqrt(5)), 0, 0, 
+   1/2*(7 + math.sqrt(5)), 0, 0, 1/2*(-3 + math.sqrt(5)), 0, 0, 
+   1/2*(7 + math.sqrt(5)), 0], [0, 5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 0, 
+   0, -1, 0, 0, 2*(3 + math.sqrt(5)), 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
+    0], [0, 2 + math.sqrt(5), 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 
+   1/2*(-3 + math.sqrt(5)), 0, 0, 3, 0], [0, 3 + math.sqrt(5), 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 3 + 2*math.sqrt(5), 
+   0], [0, 2*(2 + math.sqrt(5)), 0, 0, 2*(3 + math.sqrt(5)), 0, 0, -1, 0, 0, 
+   2*(3 + math.sqrt(5)), 0], [0, 2 + math.sqrt(5), 0, 0, 3, 0, 0, 
+   1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(7 + math.sqrt(5)), 0], [0, 5 + 2*math.sqrt(5),
+    0, 0, 2*(3 + math.sqrt(5)), 0, 0, -1, 0, 0, 5 + 2*math.sqrt(5), 0], [0, 0, 
+   0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 3 + math.sqrt(5), 0, 0, 
+   3 + 2*math.sqrt(5), 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 
+   0]]), np.array([[0, 0, 0, 2 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 
+   1/2*(3 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0], [0, 0, 0, 5 + 2*math.sqrt(5), 
+   0, 1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 0, 1/2*(13 + 5*math.sqrt(5)),
+    0, 0], [0, 0, 0, 3 + math.sqrt(5), 0, -1, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
+   0], [0, 0, 0, 2*(2 + math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5)), 0, 
+   5 + 2*math.sqrt(5), 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0], [0, 0, 0, 
+   3 + math.sqrt(5), 0, -1, 0, 3 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0], [0, 
+   0, 0, 2 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 
+   1/2*(5 + math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0,
+    0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, -1, 0, 3 + math.sqrt(5), 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
+   0], [0, 0, 0, 5 + 2*math.sqrt(5), 0, 1/2*(-1 - math.sqrt(5)), 0, 
+   5 + 2*math.sqrt(5), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0], [0, 0, 0, 
+   1/2*(3 + math.sqrt(5)), 0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 
+   3 + math.sqrt(5), 0, 0]]), np.array([[0, 0, 1/2*(-1 - math.sqrt(5)), 0, 
+   1/2*(7 + 3*math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 
+   1/2*(7 + 3*math.sqrt(5))], [0, 0, -1, 0, 3 + math.sqrt(5), 1/2*(5 + math.sqrt(5)),
+    0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5))], [0, 0, -1, 0, 3 + math.sqrt(5), 2, 
+   0, 0, 0, 0, 0, 3 + math.sqrt(5)], [0, 0, 1/2*(-3 - math.sqrt(5)), 0, 
+   1/2*(11 + 5*math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 
+   1/2*(13 + 5*math.sqrt(5))], [0, 0, 0, 0, 1, 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, 
+   1/2*(13 + 5*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 
+   1/2*(13 + 5*math.sqrt(5))], [0, 0, 1/2*(-1 - math.sqrt(5)), 0, 
+   1/2*(7 + 3*math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0, 
+   2*(2 + math.sqrt(5))], [0, 0, 1/2*(-3 - math.sqrt(5)), 0, 
+   1/2*(13 + 5*math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 
+   1/2*(11 + 5*math.sqrt(5))], [0, 0, -1, 0, 1/2*(5 + math.sqrt(5)), 
+   1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 3 + math.sqrt(5)], [0, 0, 
+   1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 0, 0,
+    1/2*(7 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0, 
+   0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 3 + 2*math.sqrt(5), 
+   1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 3, 0, 
+   1/2*(7 + math.sqrt(5)), 1/2*(-3 + math.sqrt(5)), 2 + math.sqrt(5), 0], [0, 0, 0, 
+   0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 3, 1/2*(-3 + math.sqrt(5)), 2 + math.sqrt(5), 
+   0], [0, 0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 1/2*(7 + math.sqrt(5)), 
+   1/2*(-3 + math.sqrt(5)), 1/2*(3 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(5 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)), 
+   1/2*(7 + 3*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 5 + 2*math.sqrt(5), 0, 
+   2*(3 + math.sqrt(5)), -1, 5 + 2*math.sqrt(5), 0], [0, 0, 0, 0, 0, 0, 1, 0, 0,
+    0, 0, 0], [0, 0, 0, 0, 0, 0, 3 + 2*math.sqrt(5), 0, 
+   1/2*(5 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)), 3 + math.sqrt(5), 0], [0, 0, 0, 
+   0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 
+   2*(3 + math.sqrt(5)), -1, 2*(2 + math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 
+   0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 
+   5 + 2*math.sqrt(5), -1, 5 + 2*math.sqrt(5), 0]]), np.array([[0, 0, 0, 0, 0, 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 1/2*(1 - math.sqrt(5)), 
+   1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 5 + 2*math.sqrt(5), 0, 
+   5 + 2*math.sqrt(5), -1, 2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 
+   1/2*(7 + math.sqrt(5)), 0, 1/2*(3 + math.sqrt(5)), 1/2*(-3 + math.sqrt(5)), 
+   1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 
+   2 + math.sqrt(5), 1/2*(-3 + math.sqrt(5)), 3], [0, 0, 0, 0, 0, 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 0, 3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)), 
+   3 + 2*math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 3, 0, 2 + math.sqrt(5), 
+   1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 
+   3 + 2*math.sqrt(5), 0, 3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)), 
+   1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 
+   0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 5 + 2*math.sqrt(5), -1, 
+   5 + 2*math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 
+   0, 0, 0, 2*(3 + math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), -1, 
+   2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0, 0, 0,
+    2*(2 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 1/2*(7 + 3*math.sqrt(5)), 0, 
+   1/2*(-1 - math.sqrt(5)), 0, 0], [0, 0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 
+   3/2*(3 + math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 0, 1/2*(-3 - math.sqrt(5)), 0, 
+   0], [0, 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 1/2*(5 + math.sqrt(5)), 
+   3 + math.sqrt(5), 0, -1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
+   0], [0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 3/2*(3 + math.sqrt(5)), 
+   1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-3 - math.sqrt(5)), 0, 0], [0, 0, 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 
+   1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-3 - math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0,
+    0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0,
+    0, 3 + math.sqrt(5), 0, 0, 1/2*(5 + math.sqrt(5)), 1/2*(5 + math.sqrt(5)), 0, -1,
+    0, 0], [0, 0, 0, 3 + math.sqrt(5), 0, 0, 2, 3 + math.sqrt(5), 0, -1, 0, 
+   0], [0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 1/2*(5 + 3*math.sqrt(5)), 
+   1/2*(7 + 3*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5)), 0, 0], [0, 0, 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 2*(2 + math.sqrt(5)), 0, 
+   1/2*(-1 - math.sqrt(5)), 0, 0]]), np.array([[0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 
+   3/2*(3 + math.sqrt(5))], [0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 2*(2 + math.sqrt(5)),
+    0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2 + math.sqrt(5)], [0, 0, 1, 0, 0, 
+   0, 0, 0, 0, 0, 0, 0], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 
+   1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 
+   3/2*(3 + math.sqrt(5))], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 
+   1/2*(5 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0, -1, 
+   1/2*(5 + math.sqrt(5))], [0, 0, 2*(2 + math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)),
+    0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2 + math.sqrt(5)], [0, 0, 
+   3 + math.sqrt(5), 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, -1, 
+   1/2*(5 + math.sqrt(5))], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-3 - math.sqrt(5)), 
+   1/2*(7 + 3*math.sqrt(5))], [0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
+   1/2*(5 + 3*math.sqrt(5))], [0, 0, 3 + math.sqrt(5), 0, 3 + math.sqrt(5), 0, 0, 0, 
+   0, 0, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[0, 
+   1/2*(-1 - math.sqrt(5)), 2*(2 + math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 
+   0, 1/2*(13 + 5*math.sqrt(5)), 0], [0, -1, 3 + math.sqrt(5), 0, 0, 0, 
+   3 + math.sqrt(5), 0, 0, 0, 2*(2 + math.sqrt(5)), 0], [0, 0, 1, 0, 0, 0, 0, 0,
+    0, 0, 0, 0], [0, -1, 3 + math.sqrt(5), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0,
+    0, 0, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 1/2*(1 - math.sqrt(5)), 2 + math.sqrt(5),
+    0, 0, 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 3 + math.sqrt(5), 0], [0, 
+   1/2*(-1 - math.sqrt(5)), 5 + 2*math.sqrt(5), 0, 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 
+   0, 1/2*(13 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
+   0], [0, 1/2*(1 - math.sqrt(5)), 2 + math.sqrt(5), 0, 0, 0, 2 + math.sqrt(5), 0, 0,
+    0, 1/2*(5 + math.sqrt(5)), 0], [0, 1/2*(1 - math.sqrt(5)), 
+   1/2*(3 + math.sqrt(5)), 0, 0, 0, 2 + math.sqrt(5), 0, 0, 0, 3 + math.sqrt(5), 
+   0], [0, 1/2*(-1 - math.sqrt(5)), 5 + 2*math.sqrt(5), 0, 0, 0, 5 + 2*math.sqrt(5), 
+   0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
+   1, 0], [0, -1, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 3 + math.sqrt(5), 0, 0, 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0]]), np.array([[0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 
+   1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 
+   3/2*(3 + math.sqrt(5))], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 
+   1/2*(-3 - math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 
+   3/2*(3 + math.sqrt(5))], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 2*(2 + math.sqrt(5)), 
+   0, 0, 0, 2 + math.sqrt(5)], [0, 0, 3 + math.sqrt(5), 0, 0, 0, -1, 
+   1/2*(5 + math.sqrt(5)), 0, 0, 0, 1/2*(5 + math.sqrt(5))], [0, 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5))], [0, 0, 
+   3 + math.sqrt(5), 0, 0, 0, -1, 3 + math.sqrt(5), 0, 0, 0, 2], [0, 0, 0, 0, 0,
+    0, 0, 1, 0, 0, 0, 0], [0, 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 
+   1/2*(-3 - math.sqrt(5)), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 
+   1/2*(7 + 3*math.sqrt(5))], [0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, -1, 
+   3 + math.sqrt(5), 0, 0, 0, 1/2*(5 + math.sqrt(5))], [0, 0, 2*(2 + math.sqrt(5)), 
+   0, 0, 0, 1/2*(-1 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 
+   2 + math.sqrt(5)], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]), np.array([[-1, 0, 
+   2*(2 + math.sqrt(5)), 0, 0, 0, 2*(3 + math.sqrt(5)), 2*(3 + math.sqrt(5)), 0, 0, 
+   0, 0], [-1, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 2*(3 + math.sqrt(5)), 
+   5 + 2*math.sqrt(5), 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
+   0], [1/2*(-3 + math.sqrt(5)), 0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 
+   1/2*(7 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 0, 0, 0, 
+   0], [1/2*(1 - math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 0], [-1, 0, 
+   5 + 2*math.sqrt(5), 0, 0, 0, 5 + 2*math.sqrt(5), 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, 1, 
+   0, 0, 0, 0], [1/2*(1 - math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0, 
+   3 + 2*math.sqrt(5), 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 
+   0], [1/2*(1 - math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 3 + 2*math.sqrt(5), 0, 0, 0, 
+   0], [1/2*(-3 + math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 0, 0, 
+   1/2*(7 + math.sqrt(5)), 3, 0, 0, 0, 0], [1/2*(-3 + math.sqrt(5)), 0, 
+   2 + math.sqrt(5), 0, 0, 0, 3, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 0]]), np.array([[1, 0, 
+   0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1/2*(7 + 3*math.sqrt(5)), 0, 0, 
+   3 + math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 
+   0, -1], [2*(2 + math.sqrt(5)), 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5))], [0, 0, 0, 1, 0, 0, 0,
+    0, 0, 0, 0, 0], [5 + 2*math.sqrt(5), 0, 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0,
+    0, 1/2*(13 + 5*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5))], [2 + math.sqrt(5), 0, 
+   0, 1/2*(3 + math.sqrt(5)), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 
+   1/2*(1 - math.sqrt(5))], [3 + math.sqrt(5), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 
+   0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, -1], [1/2*(3 + math.sqrt(5)), 0, 0, 
+   2 + math.sqrt(5), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0, 
+   1/2*(1 - math.sqrt(5))], [2 + math.sqrt(5), 0, 0, 2 + math.sqrt(5), 0, 0, 0, 0, 0,
+    1/2*(5 + math.sqrt(5)), 0, 1/2*(1 - math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0, 0,
+    0, 1, 0, 0], [5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 0, 0, 
+   1/2*(11 + 5*math.sqrt(5)), 0, 1/2*(-1 - math.sqrt(5))], [3 + math.sqrt(5), 0, 0, 
+   3 + math.sqrt(5), 0, 0, 0, 0, 0, 2*(2 + math.sqrt(5)), 0, -1]]), np.array([[0, 
+   2 + math.sqrt(5), 0, 0, 1/2*(3 + math.sqrt(5)), 3 + math.sqrt(5), 0, 0, 0, 
+   1/2*(1 - math.sqrt(5)), 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0,
+    3 + math.sqrt(5), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 0, 0,
+    0, -1, 0, 0], [0, 5 + 2*math.sqrt(5), 0, 0, 2*(2 + math.sqrt(5)), 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0], [0, 0, 0,
+    0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
+   0], [0, 5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 1/2*(11 + 5*math.sqrt(5)), 
+   0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0], [0, 2*(2 + math.sqrt(5)), 0, 0, 
+   5 + 2*math.sqrt(5), 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 1/2*(-1 - math.sqrt(5)), 
+   0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0], [0, 3 + math.sqrt(5), 0, 0, 
+   3 + math.sqrt(5), 2*(2 + math.sqrt(5)), 0, 0, 0, -1, 0, 0], [0, 2 + math.sqrt(5), 
+   0, 0, 2 + math.sqrt(5), 1/2*(5 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 
+   0, 0], [0, 1/2*(3 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 3 + math.sqrt(5), 0, 0,
+    0, 1/2*(1 - math.sqrt(5)), 0, 0]]), np.array([[0, 3 + math.sqrt(5), 0, 0, 0, 
+   1/2*(1 - math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 0, 1/2*(3 + math.sqrt(5)), 0], [0,
+    1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 
+   0, -1, 0, 0, 3 + math.sqrt(5), 0, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, -1, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 
+   3 + math.sqrt(5), 0], [0, 3 + math.sqrt(5), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0,
+    1/2*(3 + math.sqrt(5)), 0, 2 + math.sqrt(5), 0], [0, 2*(2 + math.sqrt(5)), 0, 0, 
+   0, -1, 0, 0, 3 + math.sqrt(5), 0, 3 + math.sqrt(5), 0], [0, 
+   1/2*(5 + math.sqrt(5)), 0, 0, 0, 1/2*(1 - math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 
+   0, 2 + math.sqrt(5), 0], [0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 
+   1/2*(-1 - math.sqrt(5)), 0, 0, 5 + 2*math.sqrt(5), 0, 5 + 2*math.sqrt(5), 0], [0, 
+   0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 
+   0, 1/2*(-1 - math.sqrt(5)), 0, 0, 5 + 2*math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 
+   0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 1/2*(13 + 5*math.sqrt(5)),
+    0, 0, 0, 1/2*(-1 - math.sqrt(5)), 0, 0, 2*(2 + math.sqrt(5)), 0, 
+   5 + 2*math.sqrt(5), 0]]), np.array([[0, 1/2*(-3 - math.sqrt(5)), 1/2*(7 + 3*math.sqrt(5)), 
+   0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(13 + 5*math.sqrt(5)), 
+   0], [0, -1, 2, 0, 3 + math.sqrt(5), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0], [0, 
+   0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1/2*(-3 - math.sqrt(5)), 
+   3/2*(3 + math.sqrt(5)), 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0,
+    1/2*(-1 - math.sqrt(5)), 2 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 
+   0, 1/2*(7 + 3*math.sqrt(5)), 0], [0, -1, 1/2*(5 + math.sqrt(5)), 0, 
+   1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 0, 3 + math.sqrt(5), 0], [0, 
+   1/2*(-1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5)), 0, 1/2*(7 + 3*math.sqrt(5)), 0,
+    0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0], [0, 1/2*(-1 - math.sqrt(5)), 
+   2 + math.sqrt(5), 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 0, 
+   2*(2 + math.sqrt(5)), 0], [0, 1/2*(-3 - math.sqrt(5)), 3/2*(3 + math.sqrt(5)), 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0], [0, 
+   0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, -1, 1/2*(5 + math.sqrt(5)), 0, 
+   3 + math.sqrt(5), 0, 0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), 0]]), np.array([[1, 0, 0, 0, 
+   0, 0, 0, 0, 0, 0, 0, 0], [2 + math.sqrt(5), 0, 1/2*(-3 + math.sqrt(5)), 0, 0,
+    1/2*(7 + math.sqrt(5)), 0, 0, 0, 3, 0, 0], [2*(2 + math.sqrt(5)), 0, -1, 0, 
+   0, 2*(3 + math.sqrt(5)), 0, 0, 0, 2*(3 + math.sqrt(5)), 0, 0], [2 + math.sqrt(5), 
+   0, 1/2*(-3 + math.sqrt(5)), 0, 0, 3, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 
+   0], [3 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 0, 3 + 2*math.sqrt(5), 0, 0, 
+   0, 1/2*(5 + 3*math.sqrt(5)), 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
+   0], [5 + 2*math.sqrt(5), 0, -1, 0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 
+   2*(3 + math.sqrt(5)), 0, 0], [3 + math.sqrt(5), 0, 1/2*(1 - math.sqrt(5)), 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 3 + 2*math.sqrt(5), 0, 
+   0], [1/2*(7 + 3*math.sqrt(5)), 0, 1/2*(1 - math.sqrt(5)), 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0], [0, 0, 0,
+    0, 0, 0, 0, 0, 0, 1, 0, 0], [5 + 2*math.sqrt(5), 0, -1, 0, 0, 
+   2*(3 + math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), 0, 0], [1/2*(3 + math.sqrt(5)),
+    0, 1/2*(-3 + math.sqrt(5)), 0, 0, 1/2*(7 + math.sqrt(5)), 0, 0, 0, 
+   1/2*(7 + math.sqrt(5)), 0, 0]]), np.array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
+   0], [3 + math.sqrt(5), 0, 0, 1/2*(5 + math.sqrt(5)), 0, 0, 0, 0, 
+   1/2*(5 + math.sqrt(5)), -1, 0, 0], [1/2*(11 + 5*math.sqrt(5)), 0, 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 3/2*(3 + math.sqrt(5)), 
+   1/2*(-3 - math.sqrt(5)), 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
+   0], [1/2*(13 + 5*math.sqrt(5)), 0, 0, 1/2*(11 + 5*math.sqrt(5)), 0, 0, 0, 0, 
+   3/2*(3 + math.sqrt(5)), 1/2*(-3 - math.sqrt(5)), 0, 0], [2*(2 + math.sqrt(5)), 0, 
+   0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 2 + math.sqrt(5), 
+   1/2*(-1 - math.sqrt(5)), 0, 0], [1/2*(5 + math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 
+   0, 0, 0, 0, 1/2*(5 + math.sqrt(5)), -1, 0, 0], [1/2*(7 + 3*math.sqrt(5)), 0, 
+   0, 2*(2 + math.sqrt(5)), 0, 0, 0, 0, 2 + math.sqrt(5), 1/2*(-1 - math.sqrt(5)), 0,
+    0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [3 + math.sqrt(5), 0, 0, 
+   3 + math.sqrt(5), 0, 0, 0, 0, 2, -1, 0, 0], [1/2*(7 + 3*math.sqrt(5)), 0, 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 
+   1/2*(-1 - math.sqrt(5)), 0, 0], [1/2*(13 + 5*math.sqrt(5)), 0, 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 
+   1/2*(-3 - math.sqrt(5)), 0, 0]]), np.array([[0, 0, 0, 0, 0, 1/2*(7 + math.sqrt(5)), 0, 
+   0, 0, 2 + math.sqrt(5), 1/2*(-3 + math.sqrt(5)), 3], [0, 0, 0, 0, 0, 
+   3 + 2*math.sqrt(5), 0, 0, 0, 3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)), 
+   1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 1/2*(5 + 3*math.sqrt(5)), 0, 0, 0,
+    3 + math.sqrt(5), 1/2*(1 - math.sqrt(5)), 3 + 2*math.sqrt(5)], [0, 0, 0, 0, 0, 
+   1/2*(5 + 3*math.sqrt(5)), 0, 0, 0, 1/2*(7 + 3*math.sqrt(5)), 
+   1/2*(1 - math.sqrt(5)), 1/2*(5 + 3*math.sqrt(5))], [0, 0, 0, 0, 0, 
+   1/2*(7 + math.sqrt(5)), 0, 0, 0, 1/2*(3 + math.sqrt(5)), 1/2*(-3 + math.sqrt(5)), 
+   1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0,
+    0, 0, 5 + 2*math.sqrt(5), 0, 0, 0, 5 + 2*math.sqrt(5), -1, 
+   2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 3, 0, 0, 0, 2 + math.sqrt(5), 
+   1/2*(-3 + math.sqrt(5)), 1/2*(7 + math.sqrt(5))], [0, 0, 0, 0, 0, 
+   2*(3 + math.sqrt(5)), 0, 0, 0, 5 + 2*math.sqrt(5), -1, 5 + 2*math.sqrt(5)], [0, 0,
+    0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 2*(3 + math.sqrt(5)), 0,
+    0, 0, 2*(2 + math.sqrt(5)), -1, 2*(3 + math.sqrt(5))], [0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 1]]), np.array([[0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 0, 
+   1/2*(3 + math.sqrt(5)), 0, 3 + math.sqrt(5), 0, 0, 0], [0, -1, 0, 
+   3 + math.sqrt(5), 0, 0, 3 + math.sqrt(5), 0, 2*(2 + math.sqrt(5)), 0, 0, 
+   0], [0, -1, 0, 3 + math.sqrt(5), 0, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
+   0], [0, 1/2*(-1 - math.sqrt(5)), 0, 2*(2 + math.sqrt(5)), 0, 0, 
+   5 + 2*math.sqrt(5), 0, 1/2*(13 + 5*math.sqrt(5)), 0, 0, 0], [0, 
+   1/2*(-1 - math.sqrt(5)), 0, 5 + 2*math.sqrt(5), 0, 0, 2*(2 + math.sqrt(5)), 0, 
+   1/2*(13 + 5*math.sqrt(5)), 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
+   0], [0, 1/2*(1 - math.sqrt(5)), 0, 2 + math.sqrt(5), 0, 0, 2 + math.sqrt(5), 0, 
+   1/2*(5 + math.sqrt(5)), 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
+   0], [0, -1, 0, 1/2*(7 + 3*math.sqrt(5)), 0, 0, 3 + math.sqrt(5), 0, 
+   1/2*(7 + 3*math.sqrt(5)), 0, 0, 0], [0, 1/2*(1 - math.sqrt(5)), 0, 
+   1/2*(3 + math.sqrt(5)), 0, 0, 2 + math.sqrt(5), 0, 3 + math.sqrt(5), 0, 0, 0], [0,
+    1/2*(-1 - math.sqrt(5)), 0, 5 + 2*math.sqrt(5), 0, 0, 5 + 2*math.sqrt(5), 0, 
+   1/2*(11 + 5*math.sqrt(5)), 0, 0, 0]])]
+
+    root = Node([-1, 2, 10 + 3*math.sqrt(5), 4 + math.sqrt(5), 1/(1 - 2/math.sqrt(5)), 2, 7 + 
+ 3*math.sqrt(5), 7 + 
+ 3*math.sqrt(5), 1/2*(7 + math.sqrt(5)), 1/2*(7 + math.sqrt(5)), 1/2*(11 + 
+   5*math.sqrt(5)), 1/2*(11 + 5*math.sqrt(5))], [], words, False)
+
+    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):
+        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 = 1500
+    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])*19)
+    secantMethod(matrix,matrix.shape[0],1,1.33,1.34,10**(-10),1000)
+
+    print("total (s): %f\ntotal (m): %f" % (time.time()-start, (time.time()-start)/60))
+
+main()
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