def test_Tr():
A, B = symbols('A B', commutative=False)
t = Tr(A * B)
assert str(t) == 'Tr(A*B)'
def test_permute():
A, B, C, D, E, F, G = symbols('A B C D E F G', commutative=False)
t = Tr(A * B * C * D * E * F * G)
assert t.permute(0).args[0].args == (A, B, C, D, E, F, G)
assert t.permute(2).args[0].args == (F, G, A, B, C, D, E)
assert t.permute(4).args[0].args == (D, E, F, G, A, B, C)
assert t.permute(6).args[0].args == (B, C, D, E, F, G, A)
assert t.permute(8).args[0].args == t.permute(1).args[0].args
assert t.permute(-1).args[0].args == (B, C, D, E, F, G, A)
assert t.permute(-3).args[0].args == (D, E, F, G, A, B, C)
assert t.permute(-5).args[0].args == (F, G, A, B, C, D, E)
assert t.permute(-8).args[0].args == t.permute(-1).args[0].args
t = Tr((A + B) * (B * B) * C * D)
assert t.permute(2).args[0].args == (C, D, (A + B), (B**2))
t1 = Tr(A * B)
t2 = t1.permute(1)
assert id(t1) != id(t2) and t1 == t2
def test_permute():
A, B, C, D, E, F, G = symbols('A B C D E F G', commutative=False)
t = Tr(A*B*C*D*E*F*G)
assert t.permute(0).args[0].args == (A, B, C, D, E, F, G)
assert t.permute(2).args[0].args == (F, G, A, B, C, D, E)
assert t.permute(4).args[0].args == (D, E, F, G, A, B, C)
assert t.permute(6).args[0].args == (B, C, D, E, F, G, A)
assert t.permute(8).args[0].args == t.permute(1).args[0].args
assert t.permute(-1).args[0].args == (B, C, D, E, F, G, A)
assert t.permute(-3).args[0].args == (D, E, F, G, A, B, C)
assert t.permute(-5).args[0].args == (F, G, A, B, C, D, E)
assert t.permute(-8).args[0].args == t.permute(-1).args[0].args
t = Tr((A + B)*(B*B)*C*D)
assert t.permute(2).args[0].args == (C, D, (A + B), (B**2))
t1 = Tr(A*B)
t2 = t1.permute(1)
assert id(t1) != id(t2) and t1 == t2
def test_trace_new():
a, b, c, d, Y = symbols('a b c d Y')
A, B, C, D = symbols('A B C D', commutative=False)
assert Tr(a + b) == a + b
assert Tr(A + B) == Tr(A) + Tr(B)
# check trace args not implicitly permuted
assert Tr(C * D * A * B).args[0].args == (C, D, A, B)
# check for mul and adds
assert Tr((a * b) + (c * d)) == (a * b) + (c * d)
# Tr(scalar*A) = scalar*Tr(A)
assert Tr(a * A) == a * Tr(A)
assert Tr(a * A * B * b) == a * b * Tr(A * B)
# since A is symbol and not commutative
assert isinstance(Tr(A), Tr)
# POW
assert Tr(pow(a, b)) == a**b
assert isinstance(Tr(pow(A, a)), Tr)
# Matrix
M = Matrix([[1, 1], [2, 2]])
assert Tr(M) == 3
# test indices in different forms
# no index
t = Tr(A)
assert t.args[1] == Tuple()
# single index
t = Tr(A, 0)
assert t.args[1] == Tuple(0)
# index in a list
t = Tr(A, [0])
assert t.args[1] == Tuple(0)
t = Tr(A, [0, 1, 2])
assert t.args[1] == Tuple(0, 1, 2)
# index is tuple
t = Tr(A, (0))
assert t.args[1] == Tuple(0)
t = Tr(A, (1, 2))
assert t.args[1] == Tuple(1, 2)
# trace indices test
t = Tr((A + B), [2])
assert t.args[0].args[1] == Tuple(2) and t.args[1].args[1] == Tuple(2)
t = Tr(a * A, [2, 3])
assert t.args[1].args[1] == Tuple(2, 3)
# class with trace method defined
# to simulate numpy objects
class Foo:
def trace(self):
return 1
assert Tr(Foo()) == 1
# argument test
# check for value error, when either/both arguments are not provided
pytest.raises(ValueError, lambda: Tr())
pytest.raises(ValueError, lambda: Tr(A, 1, 2))
# non-Expr objects
assert isinstance(Tr(None), Tr)