def test_subs():
A = ImmutableMatrix([[1, 2], [3, 4]])
B = ImmutableMatrix([[1, 2], [x, 4]])
C = ImmutableMatrix([[-x, x * y], [-(x + y), y**2]])
assert B.subs({x: 3}) == A
assert (x * B).subs({x: 3}) == 3 * A
assert (x * eye(2) + B).subs({x: 3}) == 3 * eye(2) + A
assert C.subs({x: -1, y: -2}) == A
assert C.subs({x: y - 1, y: x - 1}, simultaneous=True) == \
ImmutableMatrix([[1 - y, (x - 1)*(y - 1)], [2 - x - y, (x - 1)**2]])
def test_subs():
A = ImmutableMatrix([[1, 2], [3, 4]])
B = ImmutableMatrix([[1, 2], [x, 4]])
C = ImmutableMatrix([[-x, x*y], [-(x + y), y**2]])
assert B.subs({x: 3}) == A
assert (x*B).subs({x: 3}) == 3*A
assert (x*eye(2) + B).subs({x: 3}) == 3*eye(2) + A
assert C.subs({x: -1, y: -2}) == A
assert C.subs({x: y - 1, y: x - 1}, simultaneous=True) == \
ImmutableMatrix([[1 - y, (x - 1)*(y - 1)], [2 - x - y, (x - 1)**2]])
def test_Equality():
assert Equality(IM, IM) is true
assert Unequality(IM, IM) is false
assert Equality(IM, IM.subs({1: 2})) is false
assert Unequality(IM, IM.subs({1: 2})) is true
assert Equality(IM, 2) is false
assert Unequality(IM, 2) is true
M = ImmutableMatrix([x, y])
assert Equality(M, IM) is false
assert Unequality(M, IM) is true
assert Equality(M, M.subs({x: 2})).subs({x: 2}) is true
assert Unequality(M, M.subs({x: 2})).subs({x: 2}) is false
assert Equality(M, M.subs({x: 2})).subs({x: 3}) is false
assert Unequality(M, M.subs({x: 2})).subs({x: 3}) is true
def test_Equality():
assert Equality(IM, IM) is true
assert Unequality(IM, IM) is false
assert Equality(IM, IM.subs({1: 2})) is false
assert Unequality(IM, IM.subs({1: 2})) is true
assert Equality(IM, 2) is false
assert Unequality(IM, 2) is true
M = ImmutableMatrix([x, y])
assert Equality(M, IM) is false
assert Unequality(M, IM) is true
assert Equality(M, M.subs({x: 2})).subs({x: 2}) is true
assert Unequality(M, M.subs({x: 2})).subs({x: 2}) is false
assert Equality(M, M.subs({x: 2})).subs({x: 3}) is false
assert Unequality(M, M.subs({x: 2})).subs({x: 3}) is true
def test_Equality():
assert Equality(IM, IM) is S.true
assert Unequality(IM, IM) is S.false
assert Equality(IM, IM.subs(1, 2)) is S.false
assert Unequality(IM, IM.subs(1, 2)) is S.true
assert Equality(IM, 2) is S.false
assert Unequality(IM, 2) is S.true
M = ImmutableMatrix([x, y])
assert Equality(M, IM) is S.false
assert Unequality(M, IM) is S.true
assert Equality(M, M.subs(x, 2)).subs(x, 2) is S.true
assert Unequality(M, M.subs(x, 2)).subs(x, 2) is S.false
assert Equality(M, M.subs(x, 2)).subs(x, 3) is S.false
assert Unequality(M, M.subs(x, 2)).subs(x, 3) is S.true