def test_add_elementwise(self):
c = Polynomial([0])
a = [Element(0), Element(2), Element(1)]
b = [Element(1), Element(2), Element(2)]
elements = c._add_elementwise(a, b)
self.assertEqual([1, 1, 0], [e.element for e in elements])
def test_pow(self):
c = Polynomial([2, 0, 1])
c = pow(c, 0)
self.assertEqual(c.tolist(), [1])
c = Polynomial([2, 0, 1])
c = pow(c, 3)
self.assertEqual(c.tolist(), [2, 0, 0, 0, 0, 0, 1])
def test_multiply_element_to_polynomial(self):
a = Polynomial([0])
e = a._multiply_element_to_polynomial(Polynomial([1, 0, 2]),
Element(2))
p = a._elements_to_polynomial(e)
self.assertEqual(p.tolist(), [2, 0, 1])
e = a._multiply_element_to_polynomial(Polynomial([2, 2, 2, 1]),
Element(2))
p = a._elements_to_polynomial(e)
self.assertEqual(p.tolist(), [1, 1, 1, 2])
def test_tomonic(self):
a = Polynomial([2, 0, 2, 1])
a = a.tomonic()
self.assertEqual(a.tolist(), [1, 0, 1, 2])
a = Polynomial([1, 0, 2, 1])
a.tomonic()
self.assertEqual(a.tolist(), [1, 0, 2, 1])
if delta > base**power - 1:
print 'Delta must be <=', base**power - 1
sys.exit(1)
# Generate $GF(q^n)$ for $q=base $n$=power and find our root of unity
GFqn = GFpoly(base, power)
alpha = nth_root_of_unity(GFqn, base**power - 1)
# Calculate the generator polynomial $G(x) = \prod_{i=1}^{\delta}{(x - \alpha^i)}$
Gpoly = Polynomial((GFqn(1),))
for b in range(1, delta):
Gpoly *= Polynomial((-(alpha ** b), GFqn(1)))
codeword_len = base**power - 1
message_len = base**power - len(Gpoly)
# Compute the codeword corresponding to the message [1, 2, ... message_len]
message = Polynomial([GFqn(i + 1) for i in range(message_len)])
codeword = message * Gpoly
print 'Alpha =', alpha.tonumber()
print 'g(x) =', Gpoly
print 'Message', message.asvector(), 'maps to', codeword.asvector()
print 'message % g(x) =', message % Gpoly
print 'codeword % g(x) =', codeword % Gpoly
maxErrors = (codeword_len - message_len) // 2
print 'Can detect', codeword_len - message_len, 'errors'
print 'Can correct', maxErrors, 'errors'
def test_remove_trailing_zeros(self):
a = Polynomial([0, 0, 2, 1])
self.assertEqual(a.tolist(), [2, 1])
a = Polynomial([0, 0, 0, 0])
self.assertEqual(a.tolist(), [0])
def test_init(self):
a = Polynomial([1, 1, 2, 0, 1])
self.assertEqual(a.tolist(), [1, 1, 2, 0, 1])
def test_complement(self):
a = Polynomial([1, 2, 0])
c = a.complement()
self.assertEqual(c.tolist(), [2, 1, 0])
sys.exit(1)
base = int(sys.argv[1])
power = int(sys.argv[2])
delta = int(sys.argv[3])
if delta > base**power - 1:
print 'Delta must be <=', base**power - 1
sys.exit(1)
# Generate $GF(q^n)$ for $q=base $n$=power and find our root of unity
GFqn = GFpoly(base, power)
alpha = nth_root_of_unity(GFqn, base**power - 1)
# Calculate the generator polynomial $G(x) = \prod_{i=1}^{\delta}{(x - \alpha^i)}$
Gpoly = Polynomial((GFqn(1), ))
for b in range(1, delta):
Gpoly *= Polynomial((-(alpha**b), GFqn(1)))
codeword_len = base**power - 1
message_len = base**power - len(Gpoly)
# Compute the codeword corresponding to the message [1, 2, ... message_len]
message = Polynomial([GFqn(i + 1) for i in range(message_len)])
codeword = message * Gpoly
print 'Alpha =', alpha.tonumber()
print 'g(x) =', Gpoly
print 'Message', message.asvector(), 'maps to', codeword.asvector()
print 'message % g(x) =', message % Gpoly
print 'codeword % g(x) =', codeword % Gpoly
