def test5(self):
"""Check equivalence between multiplication with and w/o use of generator in F27
"""
f27g = finite_field(27)
f3 = finite_field(3)
f27 = FiniteField(3, 3, f3.polynomial(-1, -1, 0, 1))
for a in f27:
for b in f27:
self.assertEqual(a * b, f27g.element(a) * f27g.element(b))
if not b.null:
self.assertEqual(a / b, f27g.element(a) / f27g.element(b))
def test4(self):
"""Check equivalence between multiplication with and w/o use of generator in F25
"""
f25g = finite_field(25)
f5 = finite_field(5)
f25 = FiniteField(5, 2, f5.polynomial(2, 0, 1))
for a in f25:
for b in f25:
self.assertEqual(a * b, f25g.element(a) * f25g.element(b))
if not b.null:
self.assertEqual(a / b, f25g.element(a) / f25g.element(b))
def test3(self):
"""Check equivalence between multiplication with and w/o use of generator in F16
"""
f16g = finite_field(16)
f2 = finite_field(2)
f16 = FiniteField(2, 4, f2.polynomial(1, 1, 0, 0, 1))
for a in f16:
for b in f16:
self.assertEqual(a * b, f16g.element(a) * f16g.element(b))
if not b.null:
self.assertEqual(a / b, f16g.element(a) / f16g.element(b))
def setUp(self) -> None:
self.f2 = finite_field(2)
self.f4 = FiniteField(2, 2, self.f2.polynomial(1, 1, 1))
self.f4g = FiniteField(2,
2,
self.f2.polynomial(1, 1, 1),
generator=(0, 1))
def testFiniteFieldF4(self):
"""Check full Cantor-Zassenhaus factorization over F4
"""
f4 = finite_field(4)
p1 = f4.polynomial(1, f4(1, 1), 1)
p2 = f4.polynomial(1, f4(1, 1), 0, 1)
p3 = f4.polynomial(f4(0, 1), 1)**2
p4 = f4.polynomial(f4(0, 1), 1, f4(0, 1), 0, f4(1, 1)) / f4(1, 1)
ps = [p1, p2, p3, p4]
for p in ps:
with self.subTest(f'Testing factorizing {str(p)}'):
factors, c = factorize(p).cantor_zassenhaus()
self.assertTrue(p == factorize(p).factors_product(factors) * c)
def testFiniteFieldF9(self):
"""Check full Cantor-Zassenhaus factorization over F9
"""
f9 = finite_field(9)
p1 = f9.polynomial(1, f9(1, 1), 1)
p2 = f9.polynomial(1, f9(1, 1), 0, 1)
p3 = f9.polynomial(f9(0, 1), 1)**2
p4 = f9.polynomial(f9(0, 1), 1, f9(0, 1), 0, f9(1, 1)) / f9(1, 1)
p5 = f9.polynomial(f9(-1, 1), f9(1, -1), 1)**3
ps = [p1, p2, p3, p4, p5]
for p in ps:
with self.subTest(f'Testing factorizing {str(p)}'):
factors, c = factorize(p).cantor_zassenhaus()
self.assertTrue(p == factorize(p).factors_product(factors) * c)