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from sympy.physics.quantum import Dagger
from sympy.physics.quantum.boson import BosonOp
from sympy.physics.quantum.fermion import FermionOp
from sympy.physics.quantum.operatorordering import (normal_order,
                                                 normal_ordered_form)


def test_normal_order():
    a = BosonOp('a')

    c = FermionOp('c')

    assert normal_order(a * Dagger(a)) == Dagger(a) * a
    assert normal_order(Dagger(a) * a) == Dagger(a) * a
    assert normal_order(a * Dagger(a) ** 2) == Dagger(a) ** 2 * a

    assert normal_order(c * Dagger(c)) == - Dagger(c) * c
    assert normal_order(Dagger(c) * c) == Dagger(c) * c
    assert normal_order(c * Dagger(c) ** 2) == Dagger(c) ** 2 * c


def test_normal_ordered_form():
    a = BosonOp('a')

    c = FermionOp('c')

    assert normal_ordered_form(Dagger(a) * a) == Dagger(a) * a
    assert normal_ordered_form(a * Dagger(a)) == 1 + Dagger(a) * a
    assert normal_ordered_form(a ** 2 * Dagger(a)) == \
        2 * a + Dagger(a) * a ** 2
    assert normal_ordered_form(a ** 3 * Dagger(a)) == \
        3 * a ** 2 + Dagger(a) * a ** 3

    assert normal_ordered_form(Dagger(c) * c) == Dagger(c) * c
    assert normal_ordered_form(c * Dagger(c)) == 1 - Dagger(c) * c
    assert normal_ordered_form(c ** 2 * Dagger(c)) == Dagger(c) * c ** 2
    assert normal_ordered_form(c ** 3 * Dagger(c)) == \
        c ** 2 - Dagger(c) * c ** 3

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