from sympy import I, symbols
from sympy.physics.paulialgebra import Pauli
from sympy.utilities.pytest import XFAIL
from sympy.physics.quantum import TensorProduct

sigma1 = Pauli(1)
sigma2 = Pauli(2)
sigma3 = Pauli(3)

tau1 = symbols("tau1", commutative = False)


def test_Pauli():

    assert sigma1 == sigma1
    assert sigma1 != sigma2

    assert sigma1*sigma2 == I*sigma3
    assert sigma3*sigma1 == I*sigma2
    assert sigma2*sigma3 == I*sigma1

    assert sigma1*sigma1 == 1
    assert sigma2*sigma2 == 1
    assert sigma3*sigma3 == 1

    assert sigma1**0 == 1
    assert sigma1**1 == sigma1
    assert sigma1**2 == 1
    assert sigma1**3 == sigma1
    assert sigma1**4 == 1

    assert sigma3**2 == 1

    assert sigma1*2*sigma1 == 2


def test_evaluate_pauli_product():
    from sympy.physics.paulialgebra import evaluate_pauli_product

    assert evaluate_pauli_product(I*sigma2*sigma3) == -sigma1

    # Check issue 6471
    assert evaluate_pauli_product(-I*4*sigma1*sigma2) == 4*sigma3

    assert evaluate_pauli_product(
        1 + I*sigma1*sigma2*sigma1*sigma2 + \
        I*sigma1*sigma2*tau1*sigma1*sigma3 + \
        ((tau1**2).subs(tau1, I*sigma1)) + \
        sigma3*((tau1**2).subs(tau1, I*sigma1)) + \
        TensorProduct(I*sigma1*sigma2*sigma1*sigma2, 1)
    ) == 1 -I + I*sigma3*tau1*sigma2 - 1 - sigma3 - I*TensorProduct(1,1)


@XFAIL
def test_Pauli_should_work():
    assert sigma1*sigma3*sigma1 == -sigma3
