def testRsub(self):
# Fp - Fq
s = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(1, 1)], self.F3), self.F81)
result = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(0, 1), (1, 2)], self.F3), self.F81)
self.assertEqual(result, self.F3.one - s)
# Z -Fq
self.assertEqual(result, 1 - s)
def setUp(self):
"""
create two different Fq's.
"""
self.F2 = FinitePrimeField.getInstance(2)
f = FinitePrimeFieldPolynomial([(0, 1), (5, 1), (6, 1)], self.F2)
self.F64 = FiniteExtendedField(2, f)
self.F3 = FinitePrimeField.getInstance(3)
f = FinitePrimeFieldPolynomial(enumerate([1, 2, 1, 2, 1]), self.F3)
self.F81 = FiniteExtendedField(3, f)
def testAdd(self):
s = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(1, 1)], self.F3), self.F81)
t = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(0, 1), (1, 1)], self.F3), self.F81)
result = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(0, 1), (1, 2)], self.F3), self.F81)
self.assertEqual(result, s + t)
self.assertEqual(t, s + self.F81.one)
self.assertEqual(t, s + self.F3.one)
def testSub(self):
s = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(1, 1)], self.F3), self.F81)
t = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(0, 1), (1, 1)], self.F3), self.F81)
result = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(0, 2)], self.F3), self.F81)
tluser = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(0, 1)], self.F3), self.F81)
self.assertEqual(result, s - t)
self.assertEqual(tluser, t - s)
self.assertEqual(self.F81.zero, s - s)
def testIsomorphism(self):
"""
test for fqiso
"""
g = FinitePrimeFieldPolynomial(enumerate([1, 1, 0, 0, 1, 1, 1]),
self.F2)
F64b = FiniteExtendedField(2, g)
f64iso = fqiso(self.F64, F64b)
self.assertEqual(F64b.zero, f64iso(self.F64.zero))
self.assertEqual(F64b.one, f64iso(self.F64.one))
x = F64b.createElement(2)
self.assertEqual(F64b.order(x), self.F64.order(f64iso(x)))
g = FinitePrimeFieldPolynomial(enumerate([2, 0, 0, 1, 1]), self.F3)
F81b = FiniteExtendedField(3, g)
f81iso = fqiso(self.F81, F81b)
self.assertEqual(F81b.zero, f81iso(self.F81.zero))
self.assertEqual(F81b.one, f81iso(self.F81.one))
def testCreateElement(self):
F125 = FiniteExtendedField(5, 3)
self.assertEqual(
F125.createElement(6),
F125.createElement(
FinitePrimeFieldPolynomial(enumerate([1, 1]),
FinitePrimeField.getInstance(5))))
self.assertEqual(F125.createElement(6), F125.createElement([1, 1]))
def testInit(self):
self.assertEqual(8, card(FiniteExtendedField(2, 3)))
f = FinitePrimeFieldPolynomial(enumerate([1, 1, 0, 1]),
FinitePrimeField.getInstance(2))
self.assertEqual(8, card(FiniteExtendedField(2, f)))
for i in range(10): # 10 might be enough to check random moduli
F8 = FiniteExtendedField(2, 3)
defining_polynomial = F8.modulus
self.assertTrue(defining_polynomial.degree() == 3)
self.assertTrue(defining_polynomial.isirreducible())
def testRepr(self):
f = FinitePrimeFieldPolynomial(
[(0, 2), (8, 1)], coeffring=FinitePrimeField.getInstance(311))
self.assertEqual(0, repr(f).index("Finite"))
def testNorm(self):
a3 = FiniteExtendedFieldElement(
FinitePrimeFieldPolynomial([(3, 1)], self.F3), self.F81)
self.assertTrue(a3.norm() in self.F3, repr(a3.norm()))