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 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 testContains(self):
# elements of the field
F125 = FiniteExtendedField(5, 3)
self.assertTrue(F125.one in F125)
self.assertTrue(F125.createElement(17) in F125)
# elements of prime fields
self.assertTrue(FinitePrimeField.getInstance(5).one in F125)
# different characteristic
self.assertFalse(FinitePrimeFieldElement(3, 7) in F125)
# elements of disjoint fields
F25 = FiniteExtendedField(5, 2)
self.assertFalse(F25.one in F125)
self.assertFalse(F25.createElement(17) in F125)
F625 = FiniteExtendedField(5, 4)
self.assertFalse(F625.one in F125)
self.assertFalse(F625.createElement(17) in F125)
# we don't expect an element of extended fields be in the field
# even if it actually is.
F15625 = FiniteExtendedField(5, 6)
self.assertFalse(F15625.one in F125)
def testRepr(self):
f = FinitePrimeFieldPolynomial(
[(0, 2), (8, 1)], coeffring=FinitePrimeField.getInstance(311))
self.assertEqual(0, repr(f).index("Finite"))
def testSubring(self):
F125 = FiniteExtendedField(5, 3)
F5 = FinitePrimeField.getInstance(5)
self.assertFalse(F125.issubring(F5))
def setUp(self):
self.F3 = FinitePrimeField.getInstance(3)
self.F81 = FiniteExtendedField(3, 4)
def testGetInstance(self):
self.assertEqual(self.F17, FinitePrimeField.getInstance(17))
self.assertTrue(
FinitePrimeField.getInstance(17) is FinitePrimeField.getInstance(
17))