def test_products():
assert TensorProduct(R2.dx, R2.dy)(
R2.e_x, R2.e_y) == R2.dx(R2.e_x) * R2.dy(R2.e_y) == 1
assert WedgeProduct(R2.dx, R2.dy)(R2.e_x, R2.e_y) == 1
assert TensorProduct(R2.dx, R2.dy)(None, R2.e_y) == R2.dx
assert TensorProduct(R2.dx, R2.dy)(R2.e_x, None) == R2.dy
assert TensorProduct(R2.dx, R2.dy)(R2.e_x) == R2.dy
assert TensorProduct(R2.x, R2.dx) == R2.x * R2.dx
def test_correct_arguments():
pytest.raises(ValueError, lambda: R2.e_x(R2.e_x))
pytest.raises(ValueError, lambda: R2.e_x(R2.dx))
pytest.raises(ValueError, lambda: Commutator(R2.e_x, R2.x))
pytest.raises(ValueError, lambda: Commutator(R2.dx, R2.e_x))
pytest.raises(ValueError, lambda: Differential(Differential(R2.e_x)))
pytest.raises(ValueError, lambda: R2.dx(R2.x))
pytest.raises(ValueError, lambda: TensorProduct(R2.e_x, R2.dx))
pytest.raises(ValueError, lambda: LieDerivative(R2.dx, R2.dx))
pytest.raises(ValueError, lambda: LieDerivative(R2.x, R2.dx))
pytest.raises(ValueError, lambda: CovarDerivativeOp(R2.dx, []))
pytest.raises(ValueError, lambda: CovarDerivativeOp(R2.x, []))
a = Symbol('a')
pytest.raises(ValueError, lambda: intcurve_series(R2.dx, a, R2_r.point([1, 2])))
pytest.raises(ValueError, lambda: intcurve_series(R2.x, a, R2_r.point([1, 2])))
pytest.raises(ValueError, lambda: intcurve_diffequ(R2.dx, a, R2_r.point([1, 2])))
pytest.raises(ValueError, lambda: intcurve_diffequ(R2.x, a, R2_r.point([1, 2])))
pytest.raises(ValueError, lambda: contravariant_order(R2.e_x + R2.dx))
pytest.raises(ValueError, lambda: contravariant_order(R2.dx**2))
pytest.raises(ValueError, lambda: covariant_order(R2.e_x + R2.dx))
pytest.raises(ValueError, lambda: contravariant_order(R2.e_x*R2.e_y))
pytest.raises(ValueError, lambda: covariant_order(R2.dx*R2.dy))
assert covariant_order(Integer(0), True) == -1
assert contravariant_order(Integer(0), True) == -1
def test_Differential():
tp = TensorProduct(R2.dx, R2.dy)
assert sstr(LieDerivative(R2.e_x, tp)) == 'LieDerivative(e_x, TensorProduct(dx, dy))'
g = Function('g')
s_field = g(R2.x, R2.y)
assert sstr(Differential(s_field)) == 'd(g(x, y))'
def test_lie_derivative():
assert LieDerivative(R2.e_x, R2.y) == R2.e_x(R2.y) == 0
assert LieDerivative(R2.e_x, R2.x) == R2.e_x(R2.x) == 1
assert LieDerivative(R2.e_x, R2.e_x) == Commutator(R2.e_x, R2.e_x) == 0
assert LieDerivative(R2.e_x, R2.e_r) == Commutator(R2.e_x, R2.e_r)
assert LieDerivative(R2.e_x + R2.e_y, R2.x) == 1
assert LieDerivative(R2.e_x, TensorProduct(R2.dx, R2.dy))(R2.e_x,
R2.e_y) == 0
def test_helpers_and_coordinate_dependent():
one_form = R2.dr + R2.dx
two_form = Differential(R2.x * R2.dr + R2.r * R2.dx)
three_form = Differential(R2.y * two_form) + Differential(
R2.x * Differential(R2.r * R2.dr))
metric = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dy, R2.dy)
metric_ambig = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dr, R2.dr)
misform_a = TensorProduct(R2.dr, R2.dr) + R2.dr
misform_b = R2.dr**4
misform_c = R2.dx * R2.dy
twoform_not_sym = TensorProduct(R2.dx, R2.dx) + TensorProduct(R2.dx, R2.dy)
twoform_not_TP = WedgeProduct(R2.dx, R2.dy)
assert covariant_order(one_form) == 1
assert covariant_order(two_form) == 2
assert covariant_order(three_form) == 3
assert covariant_order(two_form + metric) == 2
assert covariant_order(two_form + metric_ambig) == 2
assert covariant_order(two_form + twoform_not_sym) == 2
assert covariant_order(two_form + twoform_not_TP) == 2
pytest.raises(ValueError, lambda: covariant_order(misform_a))
pytest.raises(ValueError, lambda: covariant_order(misform_b))
pytest.raises(ValueError, lambda: covariant_order(misform_c))
assert twoform_to_matrix(metric) == Matrix([[1, 0], [0, 1]])
assert twoform_to_matrix(twoform_not_sym) == Matrix([[1, 0], [1, 0]])
assert twoform_to_matrix(twoform_not_TP) == Matrix([[0, -1], [1, 0]])
pytest.raises(ValueError, lambda: twoform_to_matrix(one_form))
pytest.raises(ValueError, lambda: twoform_to_matrix(three_form))
pytest.raises(ValueError, lambda: twoform_to_matrix(metric_ambig))
pytest.raises(ValueError,
lambda: metric_to_Christoffel_1st(twoform_not_sym))
pytest.raises(ValueError,
lambda: metric_to_Christoffel_2nd(twoform_not_sym))
pytest.raises(ValueError,
lambda: metric_to_Riemann_components(twoform_not_sym))
pytest.raises(ValueError,
lambda: metric_to_Ricci_components(twoform_not_sym))