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)
class FinitePrimeFieldTest(unittest.TestCase):
def setUp(self):
self.F17 = FinitePrimeField(17)
def testEq(self):
self.assertEqual(self.F17, self.F17)
def testNonZero(self):
self.assertTrue(self.F17)
self.assertTrue(FinitePrimeField(17L))
def testConst(self):
self.assertEqual(FinitePrimeFieldElement(1, 17), self.F17.one)
self.assertEqual(FinitePrimeFieldElement(0, 17), self.F17.zero)
self.assertEqual(self.F17.one, self.F17.one * self.F17.one)
self.assertEqual(self.F17.one, self.F17.one + self.F17.zero)
self.assertEqual(self.F17.zero, self.F17.zero * self.F17.zero)
def testGetInstance(self):
self.assertEqual(self.F17, FinitePrimeField.getInstance(17))
self.assertTrue(
FinitePrimeField.getInstance(17) is FinitePrimeField.getInstance(
17))
def testStrings(self):
self.assertEqual("F_17", str(self.F17))
self.assertEqual("FinitePrimeField(17)", repr(self.F17))
def testSubring(self):
self.assertTrue(self.F17.issubring(self.F17))
self.assertTrue(self.F17.issuperring(self.F17))
# polynomial ring
import nzmath.poly.ring as ring
F17X = ring.PolynomialRing(self.F17, 1)
self.assertTrue(self.F17.issubring(F17X))
self.assertFalse(self.F17.issuperring(F17X))
# rational field
self.assertFalse(self.F17.issuperring(theRationalField))
self.assertFalse(self.F17.issubring(theRationalField))
def testHash(self):
dictionary = {}
dictionary[self.F17] = 1
self.assertEqual(1, dictionary[FinitePrimeField(17)])
def setUp(self):
self.F17 = FinitePrimeField(17)
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 testHash(self):
dictionary = {}
dictionary[self.F17] = 1
self.assertEqual(1, dictionary[FinitePrimeField(17)])
def testGetInstance(self):
self.assertEqual(self.F17, FinitePrimeField.getInstance(17))
self.assertTrue(
FinitePrimeField.getInstance(17) is FinitePrimeField.getInstance(
17))
def testNonZero(self):
self.assertTrue(self.F17)
self.assertTrue(FinitePrimeField(17))
def testGetGroup(self):
assert (Group(PermGroup([1, 2, 3, 4]), 1) == a1.getGroup())
assert (Group(IntegerResidueClassRing(30)) == b1.getGroup())
assert (Group(FinitePrimeField(37)) == c1_a.getGroup())
assert (Group(FinitePrimeField(37), 1) == c1_m.getGroup())
def testEqual(self):
assert (aa1 == Group(Permute([2, 4, 1, 3]), 1))
assert (bb1 == Group(IntegerResidueClassRing(30)))
assert (cc1_a == Group(FinitePrimeField(37)))
assert (cc1_m == Group(FinitePrimeField(37), 1))