def test_invariants():
A = MatrixSymbol('A', n, m)
B = MatrixSymbol('B', m, l)
X = MatrixSymbol('X', n, n)
objs = [Identity(n), ZeroMatrix(m, n), A, 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_Zero_power():
z1 = ZeroMatrix(n, n)
assert z1**4 == z1
raises(ValueError, lambda: z1**-2)
assert z1**0 == Identity(n)
assert MatPow(z1, 2).doit() == z1**2
raises(ValueError, lambda: MatPow(z1, -2).doit())
z2 = ZeroMatrix(3, 3)
assert MatPow(z2, 4).doit() == z2**4
raises(ValueError, lambda: z2**-3)
assert z2**3 == MatPow(z2, 3).doit()
assert z2**0 == Identity(3)
raises(ValueError, lambda: MatPow(z2, -1).doit())
def test_identity_powers():
M = Identity(n)
assert MatPow(M, 3).doit() == M**3
assert M**n == M
assert MatPow(M, 0).doit() == M**2
assert M**-2 == M
assert MatPow(M, -2).doit() == M**0
N = Identity(3)
assert MatPow(N, 2).doit() == N**n
assert MatPow(N, 3).doit() == N
assert MatPow(N, -2).doit() == N**4
assert MatPow(N, 2).doit() == N**0
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**S.Half == sqrt(A)
raises(ShapeError, lambda: MatrixSymbol('B', 3, 2)**2)
def test_MatPow():
n = Symbol('n', integer=True)
A = MatrixSymbol('A', n, n)
assert Inverse(A).is_Pow
AA = MatPow(A, 2)
assert AA.is_Pow
assert AA.exp == 2
assert AA.base == A
assert (A**n).exp == n
assert A**0 == Identity(n)
assert A**1 == A
assert A**-1 == Inverse(A)
raises(ShapeError, lambda: MatrixSymbol('B', 3, 2)**2)
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**-1)**-1 == A
assert (A**2)**3 == A**6
assert A**S.Half == sqrt(A)
assert A**Rational(1, 3) == cbrt(A)
raises(NonSquareMatrixError, lambda: MatrixSymbol('B', 3, 2)**2)
