def __init__(self, data):
assert isinstance(data, list)
assert len(data) > 0, 'Cannot construct an empty Merkle Tree.'
num_leaves = 2**ceil(log2(len(data)))
self.data = data + [FieldElement(0)] * (num_leaves - len(data))
self.height = int(log2(num_leaves))
self.facts = {}
self.root = self.build_tree()
# a STARK proving mechanism
# from StarkWare101 Workshop
# in San Fransisco, 2/17/20
##########
# PART 1 #
##########
# first step is to create a list of length 1023
# first two elements are FieldElement objects
# representing 1 and 3141592 respectively.
a = [FieldElement(1), FieldElement(3141592)]
while len(a) < 1023:
a.append(a[-2] * a[-2] + a[-1] * a[-1])
# quick unit test to verify a[] constructed properly
assert len(a) == 1023, 'The trace must consist of exactly 1023 elements.'
assert a[0] == FieldElement(1), 'The first element in the trace must be the unit element.'
for i in range(2, 1023):
assert a[i] == a[i - 1] * a[i - 1] + a[i - 2] * a[i - 2], f'The FibonacciSq recursion rule does not apply for index {i}'
assert a[1022] == FieldElement(2338775057), 'Wrong last element!'
print('Success!')
# need a generator from field element class
# need to generator a group of size 1024
g = FieldElement.generator() ** (3 * 2 ** 20)
