def test_len(self):
v = BasisVector({})
self.assertEqual(len(v), 0)
x = Variable('x')
y = Variable('y')
v = BasisVector({x: 5, y: 2})
self.assertEqual(len(v), 2)
def test_iter(self):
x = Variable('x')
y = Variable('y')
power_dict = {x: 5, y: 2}
vector = BasisVector(power_dict)
for v, p in vector:
self.assertEqual(p, power_dict[v])
self.assertEqual(set(vector.variables()), set(power_dict))
self.assertEqual(set(vector.powers()), set(power_dict.values()))
def test_eq_ne(self):
x = Variable('x')
y = Variable('y')
z = Variable('z')
v1 = BasisVector({x: 5, y: 2, z: 3})
v2 = BasisVector({y: 2, x: 5, z: 3})
v3 = BasisVector({x: 5, z: 3})
v4 = BasisVector({x: 5, y: 0, z: 3})
self.assertTrue(v1 == v2)
self.assertTrue(v1 != v3)
self.assertTrue(v2 != v3)
self.assertTrue(v3 == v4)
def test_repr(self):
x = Variable('x')
x3 = Variable('x', 3)
v = BasisVector({x: 5, x3: 2})
self.assertEqual(v.__repr__(), '(x,5)(x_{3},2)')
self.assertEqual(v._repr_latex_(), '$(x,5)(x_{3},2)$')
# 1 if all the powers are zero.
v = BasisVector({})
self.assertEqual(v.__repr__(), '1')
self.assertEqual(v._repr_latex_(), '$1$')
def test_init(self):
# Empty initialization.
v = BasisVector({})
self.assertEqual(v.power_dict, {})
# Simple initialization.
x = Variable('x')
y = Variable('y')
power_dict = {x: 5, y: 2}
v = BasisVector(power_dict)
self.assertEqual(v.power_dict, power_dict)
# Removes zeros.
z = Variable('z')
power_dict[z] = 0
v = BasisVector(power_dict)
self.assertEqual(v.power_dict, {x: 5, y: 2})
# Non-variable variable.
with self.assertRaises(TypeError):
BasisVector({x: 5, 'y': 2})
with self.assertRaises(TypeError):
BasisVector({x: 5, 4: 2})
# Non-integer power.
power_dict[z] = 3.33
with self.assertRaises(ValueError):
BasisVector(power_dict)
def test_getter_setter(self):
# Getter.
x = Variable('x')
y = Variable('y')
z = Variable('z')
v = BasisVector({x: 5, y: 2})
self.assertEqual(v[x], 5)
self.assertEqual(v[y], 2)
self.assertEqual(v[z], 0)
self.assertEqual(len(v), 2)
with self.assertRaises(TypeError):
v['a']
# Setter.
v[x] = 12
v[z] = 6
self.assertEqual(v[x], 12)
self.assertEqual(v[y], 2)
self.assertEqual(v[z], 6)
self.assertEqual(len(v), 3)
# Delete instead of setting to zero.
v[z] = 0
self.assertEqual(v[z], 0)
self.assertEqual(len(v), 2)
# Do not set if zero.
v[z] = 0
self.assertEqual(v[z], 0)
# Non-variable variable.
with self.assertRaises(TypeError):
v['z'] = 5
with self.assertRaises(TypeError):
v[4] = 5
# Non-integer power.
with self.assertRaises(ValueError):
v[z] = 1.5
with self.assertRaises(ValueError):
v[z] = -2
def _test_basis_by_powers(self, variables, basis, basis_powers):
self.assertEqual(len(basis), len(basis_powers))
for powers in basis_powers:
v = BasisVector(dict(zip(variables, powers)))
self.assertTrue(v in basis)
def test_construct_basis(self):
# 2 variables, 3rd degree. Even and odd.
x = Variable.multivariate('x', 2)
degree = 3
basis = BasisVector.construct_basis(x, degree)
basis_powers = [(0, 0), (1, 0), (0, 1), (2, 0), (0, 2), (1, 1), (3, 0),
(0, 3), (2, 1), (1, 2)]
self._test_basis_by_powers(x, basis, basis_powers)
# 2 variables, 3rd degree. Even only.
basis = BasisVector.construct_basis(x, degree, odd=False)
basis_powers = [(0, 0), (2, 0), (0, 2), (1, 1)]
self._test_basis_by_powers(x, basis, basis_powers)
# 2 variables, 3rd degree. Odd only.
basis = BasisVector.construct_basis(x, degree, even=False)
basis_powers = [(1, 0), (0, 1), (3, 0), (0, 3), (2, 1), (1, 2)]
self._test_basis_by_powers(x, basis, basis_powers)
# 3 variables, 2nd degree. Even and odd.
x = Variable.multivariate('x', 3)
degree = 2
basis = BasisVector.construct_basis(x, degree)
basis_powers = [(0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1), (2, 0, 0),
(0, 2, 0), (0, 0, 2), (1, 1, 0), (0, 1, 1), (1, 0, 1)]
self._test_basis_by_powers(x, basis, basis_powers)
# 3 variables, 2nd degree. Even only.
basis = BasisVector.construct_basis(x, degree, odd=False)
basis_powers = [(0, 0, 0), (2, 0, 0), (0, 2, 0), (0, 0, 2), (1, 1, 0),
(0, 1, 1), (1, 0, 1)]
self._test_basis_by_powers(x, basis, basis_powers)
# 3 variables, 2nd degree. Odd only.
basis = BasisVector.construct_basis(x, degree, even=False)
basis_powers = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
self._test_basis_by_powers(x, basis, basis_powers)
# 0 degree.
degree = 0
basis = BasisVector.construct_basis(x, degree)
basis_powers = [(0, 0, 0)]
self._test_basis_by_powers(x, basis, basis_powers)
basis = BasisVector.construct_basis(x, degree, odd=False)
self._test_basis_by_powers(x, basis, basis_powers)
basis = BasisVector.construct_basis(x, degree, even=False)
basis_powers = []
self._test_basis_by_powers(x, basis, basis_powers)
# Negative degree.
with self.assertRaises(ValueError):
basis = BasisVector.construct_basis(x, -3)
# Float degree.
with self.assertRaises(ValueError):
basis = BasisVector.construct_basis(x, 3.5)
def test_degree_is_odd_is_even(self):
# Odd.
v = BasisVector({})
self.assertEqual(v.degree(), 0)
x = Variable('x')
y = Variable('y')
v = BasisVector({x: 5, y: 2})
self.assertEqual(v.degree(), 7)
self.assertTrue(v.is_odd())
self.assertFalse(v.is_even())
# Even.
v[y] = 3
self.assertEqual(v.degree(), 8)
self.assertTrue(v.is_even())
self.assertFalse(v.is_odd())
# 0 is even.
v = BasisVector({})
self.assertEqual(v.degree(), 0)
self.assertTrue(v.is_even())
self.assertFalse(v.is_odd())