def test_derivative(self):
field = FF(p=3)
polyring = Poly(field=field)
f = [field.uni(1) for i in range(11)]
self.assertEqual(polyring.derivative(f),
[field.uni(i + 1) for i in range(10)])
def test_reduce(self):
fp3 = FF(3) # X^2 - 1
self.assertEqual(fp3.reduce_poly([5]), [2])
self.assertEqual(fp3.reduce_poly([6]), [])
fp27 = FF(3, pivot=[-1, -1, 0, 1])
self.assertEqual(fp27.reduce_poly([0, 0, 0, 0, 1]), [0, 1, 1])
def test_frobenius(self):
fp27 = FF(3, pivot=[-1, -1, 0, 1])
for i in range(3):
for j in range(3):
for k in range(3):
f = [i, j, k]
f3 = fp27.mult(f, fp27.mult(f, f))
self.assertEqual(f3, fp27.frobenius(f))
def test_inverse_long(self):
fp27 = FF(3, pivot=[-1, -1, 0, 1])
for i in range(3):
for j in range(3):
for k in range(3):
if not (i == 0 and j == 0 and k == 0):
a = fp27.prune([i, j, k])
b = fp27.inv(a)
self.assertEqual(fp27.mult(a, b), [1])
def test_xn(self):
"""Test the function taking n |-> x^n"""
self.assertEqual([], FF._xn(-1, 1))
self.assertEqual([1], FF._xn(0, 1))
self.assertEqual([0, 1], FF._xn(1, 1))
self.assertEqual([0, 0, 1], FF._xn(2, 1))
f = [0 for i in range(101)]
f[-1] = 1
self.assertEqual(f, FF._xn(100, 1))
def test_inverse2(self):
fp16 = FF(2, pivot=[1, 1, 0, 0, 1])
f = [1, 1, 1]
g = fp16.inv(f)
self.assertEqual(fp16.mult(f, g), [1])
def test_inverse1(self):
fp27 = FF(3, pivot=[-1, -1, 0, 1])
a = fp27.inv([1, 1, 1])
self.assertEqual(fp27.mult(a, [1, 1, 1]), [1])
def test_inverse_Fp(self):
fp27 = FF(3, pivot=[-1, -1, 0, 1])
self.assertEqual(fp27.inverse_f_p(2), 2)
def test_mult(self):
fp27 = FF(3, pivot=[-1, -1, 0, 1])
self.assertEqual(fp27.mult([], [1, 2, 3]), [])
self.assertEqual(fp27.mult([1, 2, 3], []), [])
self.assertEqual(fp27.mult([2], [0, 2, 1]), [0, 1, 2])
self.assertEqual(fp27.mult([1, 1], [1, 1]), [1, 2, 1])
def test_element_add(self):
fp27 = FF(3, pivot=[-1, -1, 0, 1])
self.assertEqual(fp27.add([1], [1]), [2])
self.assertEqual(fp27.add([1], [2]), [])
self.assertEqual(fp27.add([1, 1], [0, 1, 2]), [1, 2, 2])
def test_div_mod(self):
self.assertEqual(FF.div_mod([0, 1, 2], [0, 1]), ([1, 2], []))
self.assertEqual(FF.div_mod([0, 1], [0, 1, 1]), ([], [0, 1]))
def test_auxilliary_add(self):
self.assertEqual(FF._add([1, 2, 3], [], 1), [1, 2, 3])
self.assertEqual(FF._add([1, 2, 3], [1, 2, 3], -1), [])
self.assertEqual(FF._add([1, 2, 3], [1, 2, 3], 2), [3, 6, 9])
self.assertEqual(FF._add([1], [4, 5, 6], 1), [5, 5, 6])
def test_prune(self):
self.assertEqual([1, 2, 3], FF.prune([1, 2, 3, 0, 0]))
self.assertEqual([], FF.prune([]))
self.assertEqual([], FF.prune([0, 0, 0]))
self.assertEqual([1, 2, 3], FF.prune([1, 2, 3]))
self.assertEqual([1, 2, 3, 0, 1], FF.prune([1, 2, 3, 0, 1, 0, 0]))
def test_inverse_short(self):
fp7 = FF(53)
for i in range(1, 7):
self.assertEqual(fp7.mult([i], fp7.inv([i])), [1])