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_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_intcurve_diffequ():
start_point = R2_r.point([1, 0])
vector_field = -R2.y*R2.e_x + R2.x*R2.e_y
equations, init_cond = intcurve_diffequ(vector_field, t, start_point)
assert sstr(equations) == '[f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p)
assert sstr(
equations) == '[Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
def test_intcurve_diffequ():
start_point = R2_r.point([1, 0])
vector_field = -R2.y*R2.e_x + R2.x*R2.e_y
equations, init_cond = intcurve_diffequ(vector_field, t, start_point)
assert sstr(equations) == '[f_1(t) + Derivative(f_0(t), t), -f_0(t) + Derivative(f_1(t), t)]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
equations, init_cond = intcurve_diffequ(vector_field, t, start_point, R2_p)
assert sstr(
equations) == '[Derivative(f_0(t), t), Derivative(f_1(t), t) - 1]'
assert sstr(init_cond) == '[f_0(0) - 1, f_1(0)]'
start_point = R2_r.point([x, y])
vector_field = R2_r.e_x
assert intcurve_series(vector_field, t, start_point,
n=3) == Matrix([[t + x], [y]])