class Homomorphism2Test(unittest.TestCase):
"""
test for homomorphisms
"""
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 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 testEmbedding(self):
"""
test for embedding
"""
F8 = FiniteExtendedField(2, 3)
embed8to64 = embedding(F8, self.F64)
self.assertEqual(self.F64.zero, embed8to64(F8.zero))
self.assertEqual(self.F64.one, embed8to64(F8.one))
x = F8.createElement(2)
self.assertEqual(F8.order(x), self.F64.order(embed8to64(x)))
def testDoubleEmbeddings(self):
"""
test for double_embeddings
"""
# linearly disjoint
F32 = FiniteExtendedField(2, 5)
e1, e2 = double_embeddings(F32, self.F64)
self.assertEqual(e1(F32.one), e2(self.F64.one))
def testEmbedding(self):
"""
test for embedding
"""
F8 = FiniteExtendedField(2, 3)
embed8to64 = embedding(F8, self.F64)
self.assertEqual(self.F64.zero, embed8to64(F8.zero))
self.assertEqual(self.F64.one, embed8to64(F8.one))
x = F8.createElement(2)
self.assertEqual(F8.order(x), self.F64.order(embed8to64(x)))
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))