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 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