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_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_add(self):
field = FF(p=5)
polyring = Poly(field=field)
f = [[0], [1]]
g = [[], [], [2]]
self.assertEqual(polyring.add(f, g), [[], [1], [2]])
def test_gcd(self):
field = FF(p=3)
polyring = Poly(field=field)
f = [[0], [1]]
g = [[], [], [2]]
self.assertEqual(polyring.gcd(f, g), f)
def test_div_mod(self):
field = FF(p=3)
polyring = Poly(field=field)
f = [[0], [1]]
g = [[], [], [2]]
self.assertEqual(polyring.div_mod(g, f), ([[], [2]], []))
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 on_click(self):
errormsg = "" # Message to append to in case of bad behaviour.
# Ensure poly_to_factor parses correctly.
p = 1
to_factor = None
pivot = None
try:
str = self.polynomialInput.toPlainText()
to_factor = parse_unbracketed(str)
except:
errormsg += "Error, cannot parse polynomial to factor.\n"
# Ensure p pares correctly.
try:
p = int(self.charpInput.toPlainText())
except:
errormsg += "Error, p is not a valid integer.\n"
# Ensure p is prime.
if not (prime(p)):
errormsg += "Error, p is not prime.\n"
# Ensure pivot parses correctly.
try:
pivot = parse_unbracketed(self.minPolyEntry.toPlainText(),
as_integer=True)
except:
errormsg += "Error, cannot parse minimal polynomial."
# Ensure pivot is irreducible.
if errormsg == "":
try:
field = FF(p, pivot=pivot)
polyring = Poly(field)
msg = factorise(to_factor, polyring)
self.outputDisplay.setText(msg)
except:
self.outputDisplay.setText(
"An error occured during factoring, please try again.")
else:
self.outputDisplay.setText(errormsg)
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_error(self):
fp27 = FF(3, pivot=[-1, -1, 0, 1])
self.assertRaises(ValueError, fp27.inverse_f_p, 3)
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_inverse_short(self):
fp7 = FF(53)
for i in range(1, 7):
self.assertEqual(fp7.mult([i], fp7.inv([i])), [1])