def test_MatPow():
A = MatrixSymbol('A', n, n)
AA = MatPow(A, 2)
assert AA.exp == 2
assert AA.base == A
assert (A**n).exp == n
assert A**0 == Identity(n)
assert A**1 == A
assert A**2 == AA
assert A**-1 == Inverse(A)
assert A**Rational(1, 2) == sqrt(A)
pytest.raises(ShapeError, lambda: MatrixSymbol('B', 3, 2)**2)
def test_invariants():
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('B', m, l)
X = MatrixSymbol('X', n, n)
objs = [
Identity(n),
ZeroMatrix(m, n),
MatMul(A, B),
MatAdd(A, A),
Transpose(A),
Adjoint(A),
Inverse(X),
MatPow(X, 2),
MatPow(X, -1),
MatPow(X, 0)
]
for obj in objs:
assert obj == obj.__class__(*obj.args)
def test_xxinv():
assert xxinv(MatMul(D, Inverse(D), D, evaluate=False)) == \
MatMul(Identity(n), D, evaluate=False)