def test_vector_mul(self):
self.assertEqual(
Zm(10, self.m),
SimpleVector([Zm(1, self.m),
Zm(2, self.m),
Zm(3, self.m)]) *
SimpleVector([Zm(3, self.m),
Zm(2, self.m),
Zm(1, self.m)]))
def test_add(self):
a = PolyUnivar([Zm(1, 31), Zm(2, 31), Zm(3, 31)])
b = PolyUnivar([Zm(30, 31), Zm(29, 31), Zm(28, 31)])
d = PolyUnivar([Zm(4, 31), Zm(6, 31), Zm(6, 31)])
self.assertEqual(a.zero(), a + b)
self.assertNotEqual(d, a + b)
def test_eq(self):
a = PolyUnivar([Zm(1, 31), Zm(2, 31), Zm(3, 31)])
b = PolyUnivar([Zm(1, 31), Zm(2, 31), Zm(34, 31)])
c = PolyUnivar([Zm(1, 31), Zm(1, 31), Zm(2, 31), Zm(3, 31)])
self.assertEqual(a, b)
self.assertNotEqual(a, c)
def test_pow(self):
a = PolyUnivar([Zm(1, 7), Zm(2, 7), Zm(3, 7)])
b = PolyUnivar([Zm(2, 7), Zm(3, 7), Zm(4, 7)])
c = PolyUnivar([Zm(2, 7), Zm(0, 7), Zm(2, 7), Zm(3, 7), Zm(5, 7)])
d = PolyUnivar([Zm(2, 7), Zm(0, 7), Zm(2, 7), Zm(3, 7), Zm(6, 7)])
self.assertEqual(c, a ** b)
self.assertEqual(c, b ** a)
self.assertNotEqual(d, a ** b)
def test_vector_linearlyIndependent(self):
self.assertTrue(
SimpleVector.linearlyIndependent([self.i, self.j, self.k]))
self.assertFalse(
SimpleVector.linearlyIndependent([
SimpleVector([Zm(1, self.m),
Zm(2, self.m),
Zm(3, self.m)]),
SimpleVector([Zm(1, self.m),
Zm(35, self.m),
Zm(9, self.m)]),
SimpleVector([Zm(34, self.m),
Zm(-23, self.m),
Zm(15, self.m)])
]))
self.assertFalse(
SimpleVector.linearlyIndependent([
SimpleVector([Zm(2, self.m),
Zm(34, self.m),
Zm(4, self.m)]),
SimpleVector([Zm(5, self.m),
Zm(6, self.m),
Zm(3, self.m)]),
SimpleVector([Zm(14, self.m),
Zm(32, self.m),
Zm(54, self.m)]),
SimpleVector([Zm(9, self.m),
Zm(8, self.m),
Zm(7, self.m)])
]))
def test_eq(self):
self.assertEqual(Zm(4, 3), Zm(1, 3))
self.assertEqual(Zm(-1, 3), Zm(2, 3))
def test_mul(self):
self.assertEqual(Zm(5, 31), Zm(9, 31) * Zm(4, 31))
def test_zero(self):
a = PolyUnivar([Zm(1, 7), Zm(2, 7), Zm(3, 7)])
self.assertEqual(a.zero() + a, a)
self.assertEqual(a.zero(), Zm(0, 7) * a)
def test_vector_rmul(self):
self.assertEqual(
SimpleVector([Zm(2, self.m),
Zm(0, self.m),
Zm(0, self.m)]),
Zm(2, self.m) * self.i)
def setUp(self):
self.m = 31
self.i = SimpleVector([Zm(1, self.m), Zm(0, self.m), Zm(0, self.m)])
self.j = SimpleVector([Zm(0, self.m), Zm(1, self.m), Zm(0, self.m)])
self.k = SimpleVector([Zm(0, self.m), Zm(0, self.m), Zm(1, self.m)])
self.c = Zm(0, self.m)
def test_inv(self):
x = Zm(4, self.m)
self.assertEqual(self.c.zero(), Zm.inv(x) + x)
def test_zero(self):
self.assertEqual(Zm(4, self.m), Zm(4, self.m) + self.c.zero())
def test_div(self):
self.assertEqual(Zm(4, 7), Zm(5, 7) / Zm(3, 7))
def test_sub(self):
self.assertEqual(Zm(1, 4), Zm(9, 4), Zm(12, 4))
def test_rmul(self):
self.assertEqual(Zm(5, 31), 9 * Zm(4, 31))
def test_mul(self):
a = PolyUnivar([Zm(1, 7), Zm(2, 7), Zm(3, 7)])
b = PolyUnivar([Zm(1, 7), Zm(2, 7), Zm(3, 7), Zm(4, 7)])
self.assertEqual(Zm(6, 7), a * b)
self.assertNotEqual(Zm(0, 7), a * b)
def test_rmul(self):
a = PolyUnivar([Zm(1, 7), Zm(2, 7), Zm(3, 7)])
b = PolyUnivar([Zm(2, 7), Zm(4, 7), Zm(-1, 7)])
c = PolyUnivar([Zm(2, 7), Zm(4, 7), Zm(0, 7)])
self.assertEqual(b, Zm(2, 7) * a)
self.assertEqual(PolyUnivar([]), Zm(0, 7) * a)
self.assertNotEqual(c, Zm(2, 7) * a)
self.assertNotEqual(c, Zm(0, 7) * a)
def test_vector_add(self):
self.assertEqual(
SimpleVector([Zm(1, self.m),
Zm(1, self.m),
Zm(1, self.m)]), self.i + self.j + self.k)
def test_linearlyIndependent(self):
a = PolyUnivar([Zm(1, 5), Zm(2, 5), Zm(3, 5)])
b = PolyUnivar([Zm(2, 5), Zm(3, 5), Zm(4, 5)])
c = PolyUnivar([Zm(3, 5), Zm(4, 5), Zm(0, 5)])
d = PolyUnivar([Zm(3, 5), Zm(0, 5), Zm(0, 5)])
self.assertTrue(a.linearlyIndependent([a, b, d]))
self.assertFalse(a.linearlyIndependent([a, b, c]))
self.assertFalse(a.linearlyIndependent([a, b, PolyUnivar([])]))
def test_add(self):
self.assertEqual(Zm(5, 4), Zm(6, 4) + Zm(3, 4))