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
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
def test_tensor_product_commutator():
assert TP(Comm(A, B), C).doit().expand(tensorproduct=True) == \
TP(A*B, C) - TP(B*A, C)
assert Comm(TP(A, B), TP(B, C)).doit() == \
TP(A, B)*TP(B, C) - TP(B, C)*TP(A, B)
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))
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).expand(commutator=True) == A * Comm(B, C) + Comm(A, C) * B
assert Comm(A + B, C).expand(commutator=True) == Comm(A, C) + Comm(B, C)
assert Comm(A, B + C).expand(commutator=True) == Comm(A, B) + Comm(A, C)
e = Comm(A, Comm(B, C)) + Comm(B, Comm(C, A)) + Comm(C, Comm(A, B))
assert e.doit().expand() == 0
def test_commutator():
c = Comm(A, B)
assert c.is_commutative == 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
