def test_MatrixSlice():
X = MatrixSymbol('X', 4, 4)
B = MatrixSlice(X, (1, 3), (1, 3))
C = MatrixSlice(X, (0, 3), (1, 3))
assert ask(Q.symmetric(B), Q.symmetric(X))
assert ask(Q.invertible(B), Q.invertible(X))
assert ask(Q.diagonal(B), Q.diagonal(X))
assert ask(Q.orthogonal(B), Q.orthogonal(X))
assert ask(Q.upper_triangular(B), Q.upper_triangular(X))
assert not ask(Q.symmetric(C), Q.symmetric(X))
assert not ask(Q.invertible(C), Q.invertible(X))
assert not ask(Q.diagonal(C), Q.diagonal(X))
assert not ask(Q.orthogonal(C), Q.orthogonal(X))
assert not ask(Q.upper_triangular(C), Q.upper_triangular(X))
def test_diagonal():
assert ask(Q.diagonal(X + Z.T + Identity(2)),
Q.diagonal(X) & Q.diagonal(Z)) is True
assert ask(Q.diagonal(ZeroMatrix(3, 3)))
assert ask(Q.lower_triangular(X) & Q.upper_triangular(X), Q.diagonal(X))
assert ask(Q.diagonal(X), Q.lower_triangular(X) & Q.upper_triangular(X))
assert ask(Q.symmetric(X), Q.diagonal(X))
assert ask(Q.triangular(X), Q.diagonal(X))
assert ask(Q.diagonal(C0x0))
assert ask(Q.diagonal(A1x1))
assert ask(Q.diagonal(A1x1 + B1x1))
assert ask(Q.diagonal(A1x1 * B1x1))
assert ask(Q.diagonal(V1.T * V2))
assert ask(Q.diagonal(V1.T * (X + Z) * V1))
assert ask(Q.diagonal(MatrixSlice(Y, (0, 1), (1, 2)))) is True
assert ask(Q.diagonal(V1.T * (V1 + V2))) is True
def test_symmetric():
assert ask(Q.symmetric(X), Q.symmetric(X))
assert ask(Q.symmetric(X*Z), Q.symmetric(X)) is None
assert ask(Q.symmetric(X*Z), Q.symmetric(X) & Q.symmetric(Z)) is True
assert ask(Q.symmetric(X + Z), Q.symmetric(X) & Q.symmetric(Z)) is True
assert ask(Q.symmetric(Y)) is False
assert ask(Q.symmetric(Y*Y.T)) is True
assert ask(Q.symmetric(Y.T*X*Y)) is None
assert ask(Q.symmetric(Y.T*X*Y), Q.symmetric(X)) is True
assert ask(Q.symmetric(X**10), Q.symmetric(X)) is True
assert ask(Q.symmetric(A1x1)) is True
assert ask(Q.symmetric(A1x1 + B1x1)) is True
assert ask(Q.symmetric(A1x1 * B1x1)) is True
assert ask(Q.symmetric(V1.T*V1)) is True
assert ask(Q.symmetric(V1.T*(V1 + V2))) is True
assert ask(Q.symmetric(V1.T*(V1 + V2) + A1x1)) is True
assert ask(Q.symmetric(MatrixSlice(Y, (0, 1), (1, 2)))) is True