Vehicle-cpp/hkpc/software/sympy/physics/quantum/tests/test_commutator.py

from sympy.core.numbers import Integer
from sympy.core.symbol import symbols

from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.commutator import Commutator as Comm
from sympy.physics.quantum.operator import Operator


a, b, c = symbols('a,b,c')
n = symbols('n', integer=True)
A, B, C, D = symbols('A,B,C,D', commutative=False)


def test_commutator():
    c = Comm(A, B)
    assert c.is_commutative is False
    assert isinstance(c, Comm)
    assert c.subs(A, C) == Comm(C, B)


def test_commutator_identities():
    assert Comm(a*A, b*B) == a*b*Comm(A, B)
    assert Comm(A, A) == 0
    assert Comm(a, b) == 0
    assert Comm(A, B) == -Comm(B, A)
    assert Comm(A, B).doit() == A*B - B*A
    assert Comm(A, B*C).expand(commutator=True) == Comm(A, B)*C + B*Comm(A, C)
    assert Comm(A*B, C*D).expand(commutator=True) == \
        A*C*Comm(B, D) + A*Comm(B, C)*D + C*Comm(A, D)*B + Comm(A, C)*D*B
    assert Comm(A, B**2).expand(commutator=True) == Comm(A, B)*B + B*Comm(A, B)
    assert Comm(A**2, C**2).expand(commutator=True) == \
        Comm(A*B, C*D).expand(commutator=True).replace(B, A).replace(D, C) == \
        A*C*Comm(A, C) + A*Comm(A, C)*C + C*Comm(A, C)*A + Comm(A, C)*C*A
    assert Comm(A, C**-2).expand(commutator=True) == \
        Comm(A, (1/C)*(1/D)).expand(commutator=True).replace(D, C)
    assert Comm(A + B, C + D).expand(commutator=True) == \
        Comm(A, C) + Comm(A, D) + Comm(B, C) + Comm(B, D)
    assert Comm(A, B + C).expand(commutator=True) == Comm(A, B) + Comm(A, C)
    assert Comm(A**n, B).expand(commutator=True) == Comm(A**n, B)

    e = Comm(A, Comm(B, C)) + Comm(B, Comm(C, A)) + Comm(C, Comm(A, B))
    assert e.doit().expand() == 0


def test_commutator_dagger():
    comm = Comm(A*B, C)
    assert Dagger(comm).expand(commutator=True) == \
        - Comm(Dagger(B), Dagger(C))*Dagger(A) - \
        Dagger(B)*Comm(Dagger(A), Dagger(C))


class Foo(Operator):

    def _eval_commutator_Bar(self, bar):
        return Integer(0)


class Bar(Operator):
    pass


class Tam(Operator):

    def _eval_commutator_Foo(self, foo):
        return Integer(1)


def test_eval_commutator():
    F = Foo('F')
    B = Bar('B')
    T = Tam('T')
    assert Comm(F, B).doit() == 0
    assert Comm(B, F).doit() == 0
    assert Comm(F, T).doit() == -1
    assert Comm(T, F).doit() == 1
    assert Comm(B, T).doit() == B*T - T*B
    assert Comm(F**2, B).expand(commutator=True).doit() == 0
    assert Comm(F**2, T).expand(commutator=True).doit() == -2*F
    assert Comm(F, T**2).expand(commutator=True).doit() == -2*T
    assert Comm(T**2, F).expand(commutator=True).doit() == 2*T
    assert Comm(T**2, F**3).expand(commutator=True).doit() == 2*F*T*F + 2*F**2*T + 2*T*F**2