Python R2.e_x示例

示例#1

文件： test_diffgeom.py 项目： Blendify/diofant

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

示例#2

文件： test_diffgeom.py 项目： skirpichev/diofant

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

示例#3

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

示例#4

文件： test_diffgeom.py 项目： skirpichev/diofant

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

示例#5

def test_functional_diffgeom_ch3():
    x0, y0 = symbols('x0, y0', extended_real=True)
    x, y, t = symbols('x, y, t', extended_real=True)
    f = Function('f')
    b1 = Function('b1')
    b2 = Function('b2')
    p_r = R2_r.point([x0, y0])

    s_field = f(R2.x, R2.y)
    v_field = b1(R2.x) * R2.e_x + b2(R2.y) * R2.e_y
    assert v_field.rcall(s_field).rcall(p_r).doit() == b1(x0) * Derivative(
        f(x0, y0), x0) + b2(y0) * Derivative(f(x0, y0), y0)

    assert R2.e_x(R2.r**2).rcall(p_r) == 2 * x0
    v = R2.e_x + 2 * R2.e_y
    s = R2.r**2 + 3 * R2.x
    assert v.rcall(s).rcall(p_r).doit() == 2 * x0 + 4 * y0 + 3

    circ = -R2.y * R2.e_x + R2.x * R2.e_y
    series = intcurve_series(circ, t, R2_r.point([1, 0]), coeffs=True)
    series_x, series_y = zip(*series)
    assert all(term == cos(t).taylor_term(i, t)
               for i, term in enumerate(series_x))
    assert all(term == sin(t).taylor_term(i, t)
               for i, term in enumerate(series_y))

示例#6

文件： test_function_diffgeom_book.py 项目： skirpichev/diofant

def test_functional_diffgeom_ch3():
    x0, y0 = symbols('x0, y0', extended_real=True)
    x, y, t = symbols('x, y, t', extended_real=True)
    f = Function('f')
    b1 = Function('b1')
    b2 = Function('b2')
    p_r = R2_r.point([x0, y0])

    s_field = f(R2.x, R2.y)
    v_field = b1(R2.x)*R2.e_x + b2(R2.y)*R2.e_y
    assert v_field.rcall(s_field).rcall(p_r).doit() == b1(
        x0)*Derivative(f(x0, y0), x0) + b2(y0)*Derivative(f(x0, y0), y0)

    assert R2.e_x(R2.r**2).rcall(p_r) == 2*x0
    v = R2.e_x + 2*R2.e_y
    s = R2.r**2 + 3*R2.x
    assert v.rcall(s).rcall(p_r).doit() == 2*x0 + 4*y0 + 3

    circ = -R2.y*R2.e_x + R2.x*R2.e_y
    series = intcurve_series(circ, t, R2_r.point([1, 0]), coeffs=True)
    series_x, series_y = zip(*series)
    assert all(term == cos(t).taylor_term(i, t)
               for i, term in enumerate(series_x))
    assert all(term == sin(t).taylor_term(i, t)
               for i, term in enumerate(series_y))