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 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 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)
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 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 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 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 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 testHash(self):
dictionary = {}
F125 = FiniteExtendedField(5, 3)
dictionary[F125] = 1
self.assertEqual(1, dictionary[FiniteExtendedField(5, 3)])
def testSubringGlobal(self):
import nzmath.rational as rational
F125 = FiniteExtendedField(5, 3)
self.assertFalse(F125.issubring(rational.theRationalField))
self.assertFalse(F125.issubring(rational.theIntegerRing))
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)