def test_scalar_conjugate(braket):
"""Test taking the complex conjugate (adjoint) of a scalar"""
Psi = KetSymbol("Psi", hs=0)
Phi = KetSymbol("Phi", hs=0)
phi = symbols('phi', real=True)
alpha = symbols('alpha')
expr = ScalarValue(1 + 1j)
assert expr.adjoint() == expr.conjugate() == 1 - 1j
assert braket.adjoint() == BraKet.create(Phi, Psi)
expr = 1j + braket
assert expr.adjoint() == expr.conjugate() == braket.adjoint() - 1j
expr = (1 + 1j) * braket
assert expr.adjoint() == expr.conjugate() == (1 - 1j) * braket.adjoint()
expr = braket**(I * phi)
assert expr.conjugate() == braket.adjoint()**(-I * phi)
expr = braket**alpha
assert expr.conjugate() == braket.adjoint()**(alpha.conjugate())
def test_scalar_real_imag(braket):
"""Test taking the real and imaginary part of a scalar"""
alpha = symbols('alpha')
a, b = symbols('a, b', real=True)
braket_dag = braket.adjoint()
expr = ScalarValue(1 + 1j)
assert (expr.real, expr.imag) == (1, 1)
expr = ScalarValue(a + I * b)
assert (expr.real, expr.imag) == (a, b)
expr = ScalarValue(alpha)
assert (expr.real, expr.imag) == expr.as_real_imag()
assert (expr.real, expr.imag) == alpha.as_real_imag()
expr = Zero
assert (expr.real, expr.imag) == (Zero, Zero)
expr = One
assert (expr.real, expr.imag) == (One, Zero)
assert braket.real == (braket + braket_dag) / 2
assert braket.imag == (I / 2) * (braket_dag - braket)
expr = braket + One + I
assert expr.real.expand().simplify_scalar() == 1 + braket.real.expand()
assert expr.imag.expand().simplify_scalar() == 1 + braket.imag.expand()
expr = I * braket
assert expr.real.expand() == (-I / 2) * braket_dag + (I / 2) * braket
assert expr.imag.expand() == braket / 2 + braket_dag / 2
expr = braket**alpha
assert expr.real == (expr.adjoint() + expr) / 2
assert expr.imag == (I / 2) * (expr.adjoint() - expr)