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| from sympy.core.containers import Tuple | |
| from sympy.core.symbol import symbols | |
| from sympy.matrices.dense import Matrix | |
| from sympy.physics.quantum.trace import Tr | |
| from sympy.testing.pytest import raises, warns_deprecated_sympy | |
| 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 | |
| raises(ValueError, lambda: Tr()) | |
| raises(ValueError, lambda: Tr(A, 1, 2)) | |
| def test_trace_doit(): | |
| a, b, c, d = symbols('a b c d') | |
| A, B, C, D = symbols('A B C D', commutative=False) | |
| #TODO: needed while testing reduced density operations, etc. | |
| 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_deprecated_core_trace(): | |
| with warns_deprecated_sympy(): | |
| from sympy.core.trace import Tr # noqa:F401 | |