Ejemplo n.º 1
0
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
Ejemplo n.º 2
0
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
Ejemplo n.º 3
0
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))'
Ejemplo n.º 4
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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
Ejemplo n.º 5
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))