def setUp(self):
self.i = SimpleVector([R(1), R(0), R(0)])
self.j = SimpleVector([R(0), R(1), R(0)])
self.k = SimpleVector([R(0), R(0), R(1)])
self.x = VectorSpace([self.i])
self.y = VectorSpace([self.j])
self.z = VectorSpace([self.k])
self.xy = VectorSpace([self.i, self.j])
self.yz = VectorSpace([self.j, self.k])
self.zx = VectorSpace([self.k, self.i])
self.xyz = VectorSpace([self.i, self.j, self.k])
def test_pow2(self):
a = PolyHomBivar([R(0), R(1), R(2), R(1)])
b = PolyHomBivar([R(1), R(1)])
c = PolyHomBivar([R(0), R(1), R(3), R(3), R(1)])
e = PolyHomBivar([R(1), R(3), R(3), R(1)])
self.assertEqual(c, a**b)
self.assertNotEqual(e, a**b)
def test_linearlyIndependent(self):
a = PolyUnivar([R(1), R(2), R(3)])
b = PolyUnivar([R(2), R(3), R(4)])
c = PolyUnivar([R(3), R(4), R(5)])
d = PolyUnivar([R(3), R(5), R(5)])
self.assertTrue(a.linearlyIndependent([a, b, d]))
self.assertFalse(a.linearlyIndependent([a, b, c]))
self.assertFalse(a.linearlyIndependent([a, b, PolyUnivar([])]))
def test_eq(self):
a = PolyUnivar([R(1), R(2), R(3)])
b = PolyUnivar([R(1), R(2), R(3)])
c = PolyUnivar([R(1), R(1), R(2), R(3)])
self.assertEqual(a, b)
self.assertNotEqual(a, c)
def test_add(self):
a = PolyUnivar([R(1), R(2), R(3)])
b = PolyUnivar([R(-1), R(2), R(3)])
c = PolyUnivar([R(4), R(6)])
d = PolyUnivar([R(4), R(6), R(6)])
self.assertEqual(c, a + b)
self.assertNotEqual(d, a + b)
def test_rmul(self):
a = PolyUnivar([R(1), R(2), R(3)])
b = PolyUnivar([R(2), R(4), R(6)])
c = PolyUnivar([R(2), R(4), R(7)])
self.assertEqual(b, R(2) * a)
self.assertEqual(PolyUnivar([]), R(0) * a)
self.assertNotEqual(c, R(2) * a)
self.assertNotEqual(c, R(0) * a)
def test_add(self):
self.assertEqual(R(42), R(29) + R(13))
def test_vector_add(self):
self.assertEqual(SimpleVector([R(1), R(1), R(1)]), self.i + self.j + self.k)
def test_lt(self):
self.assertTrue(R(20) < R(21))
self.assertFalse(R(21) < R(21))
def test_le(self):
self.assertTrue(R(20) <= R(20))
self.assertFalse(R(22) <= R(21))
def test_ge(self):
self.assertTrue(R(20) >= R(20))
self.assertFalse(R(21) >= R(22))
def test_gt(self):
self.assertTrue(R(21) > R(20))
self.assertFalse(R(21) > R(21))
def test_eq(self):
self.assertEqual(R(21), R(21))
self.assertNotEqual(R(20), R(21))
def test_vector_rmul(self):
self.assertEqual(SimpleVector([R(2), R(2), R(2)]), R(2) * SimpleVector([R(1), R(1), R(1)]))
def test_zero(self):
self.assertEqual(R(10), R(10) + self.c.zero())
def test_vector_mul(self):
self.assertEqual(R(10), SimpleVector([R(1), R(2), R(3)]) * SimpleVector([R(3), R(2), R(1)]))
def test_mul(self):
self.assertEqual(R(10), R(5) * R(2))
def test_vector_linearlyIndependent(self):
self.assertTrue(SimpleVector.linearlyIndependent([self.i, self.j, self.k]))
self.assertFalse(SimpleVector.linearlyIndependent([SimpleVector([R(1), R(2), R(3)]), SimpleVector([R(1), R(4), R(9)]), SimpleVector([R(3), R(8), R(15)])]))
self.assertFalse(SimpleVector.linearlyIndependent([SimpleVector([R(2), R(3), R(4)]), SimpleVector([R(5), R(6), R(3)]), SimpleVector([R(14), R(32), R(54)]), SimpleVector([R(9), R(8), R(7)])]))
def test_rmul(self):
self.assertEqual(R(10), 2 * R(5))
def test_mul(self):
a = PolyUnivar([R(1), R(2), R(3)])
b = PolyUnivar([R(1), R(2), R(3), R(4)])
self.assertEqual(R(20), a * b)
self.assertNotEqual(R(21), a * b)
def test_sub(self):
self.assertEqual(R(10), R(12) - R(2))
def test_zero(self):
a = PolyUnivar([R(1), R(2), R(3)])
self.assertEqual(a.zero() + a, a)
self.assertEqual(a.zero(), R(0) * a)
def test_div(self):
self.assertEqual(R(4), R(16) / R(4))
def test_pow(self):
a = PolyUnivar([R(1), R(2), R(3)])
b = PolyUnivar([R(2), R(3), R(4)])
c = PolyUnivar([R(2), R(7), R(16), R(17), R(12)])
d = PolyUnivar([R(2), R(7), R(16), R(17), R(13)])
self.assertEqual(c, a ** b)
self.assertEqual(c, b ** a)
self.assertNotEqual(d, a ** b)
def setUp(self):
# Set up unit vectors in R3
self.i = SimpleVector([R(1), R(0), R(0)])
self.j = SimpleVector([R(0), R(1), R(0)])
self.k = SimpleVector([R(0), R(0), R(1)])
self.c = R(0)
def test_pow(self):
a = PolyHomBivar([R(1), R(2), R(1)])
b = PolyHomBivar([R(1), R(1)])
self.assertEqual(a, b**b)
def test_inv(self):
self.assertEqual(R(10) + R.inv(R(10)), self.c.zero())
def test_add(self):
a = PolyHomBivar([R(1), R(2), R(3)])
b = PolyHomBivar([R(4), R(5), R(6)])
c = PolyHomBivar([R(5), R(7), R(9)])
self.assertEqual(c, a + b)
def test_contains(self):
# Check that the i + 2j lies in the xy plane
self.assertIn(self.i + R(2) * self.j, self.xy)
# Check that i + 2k does not lie in the xy planes
self.assertNotIn(self.i + R(2) * self.k, self.xy)