def test_sympyissue_12005():
e1 = Subs(Derivative(f(x), x), (x, x))
assert e1.diff(x) == Derivative(f(x), x, x)
e2 = Subs(Derivative(f(x), x), (x, x**2 + 1))
assert e2.diff(x) == 2 * x * Subs(Derivative(f(x), x, x), (x, x**2 + 1))
e3 = Subs(Derivative(f(x) + y**2 - y, y), (y, y**2))
assert e3.diff(y) == 4 * y
e4 = Subs(Derivative(f(x + y), y), (y, x**2))
assert e4.diff(y) == 0
e5 = Subs(Derivative(f(x), x), (y, y), (z, z))
assert e5.diff(x) == Derivative(f(x), x, x)
assert f(g(x)).diff(g(x), g(x)) == Subs(Derivative(f(y), y, y), (y, g(x)))
def test_sympyissue_12005():
e1 = Subs(Derivative(f(x), x), (x, x))
assert e1.diff(x) == Derivative(f(x), x, x)
e2 = Subs(Derivative(f(x), x), (x, x**2 + 1))
assert e2.diff(x) == 2*x*Subs(Derivative(f(x), x, x), (x, x**2 + 1))
e3 = Subs(Derivative(f(x) + y**2 - y, y), (y, y**2))
assert e3.diff(y) == 4*y
e4 = Subs(Derivative(f(x + y), y), (y, x**2))
assert e4.diff(y) == 0
e5 = Subs(Derivative(f(x), x), (y, y), (z, z))
assert e5.diff(x) == Derivative(f(x), x, x)
assert f(g(x)).diff(g(x), g(x)) == Subs(Derivative(f(y), y, y), (y, g(x)))
def test_sympyissue_12005():
e1 = Subs(Derivative(f(x), x), (x, ), (x, ))
assert e1.diff(x) == Derivative(f(x), x, x)
e2 = Subs(Derivative(f(x), x), (x, ), (x**2 + 1, ))
assert e2.diff(x) == 2 * x * Subs(Derivative(f(x), x, x), (x, ),
(x**2 + 1, ))
e3 = Subs(Derivative(f(x) + y**2 - y, y), (y, ), (y**2, ))
assert e3.diff(y) == 4 * y
e4 = Subs(Derivative(f(x + y), y), (y, ), (x**2))
assert e4.diff(y) == S.Zero
e5 = Subs(Derivative(f(x), x), (y, z), (y, z))
assert e5.diff(x) == Derivative(f(x), x, x)
assert f(g(x)).diff(g(x), g(x)) == Subs(Derivative(Function('f')(y), y, y),
(y, ), (g(x), ))
def test_Subs():
assert Subs(x, x, 0) == Subs(y, y, 0)
assert Subs(x, x, 0).subs(x, 1) == Subs(x, x, 0)
assert Subs(y, x, 0).subs(y, 1) == Subs(1, x, 0)
assert Subs(f(x), x, 0).doit() == f(0)
assert Subs(f(x**2), x**2, 0).doit() == f(0)
assert Subs(f(x, y, z), (x, y, z), (0, 1, 1)) != \
Subs(f(x, y, z), (x, y, z), (0, 0, 1))
assert Subs(f(x, y), (x, y, z), (0, 1, 1)) == \
Subs(f(x, y), (x, y, z), (0, 1, 2))
assert Subs(f(x, y), (x, y, z), (0, 1, 1)) != \
Subs(f(x, y) + z, (x, y, z), (0, 1, 0))
assert Subs(f(x, y), (x, y), (0, 1)).doit() == f(0, 1)
assert Subs(Subs(f(x, y), x, 0), y, 1).doit() == f(0, 1)
pytest.raises(ValueError, lambda: Subs(f(x, y), (x, y), (0, 0, 1)))
pytest.raises(ValueError, lambda: Subs(f(x, y), (x, x, y), (0, 0, 1)))
assert len(Subs(f(x, y), (x, y), (0, 1)).variables) == 2
assert Subs(f(x, y), (x, y), (0, 1)).point == Tuple(0, 1)
assert Subs(f(x), x, 0) == Subs(f(y), y, 0)
assert Subs(f(x, y), (x, y), (0, 1)) == Subs(f(x, y), (y, x), (1, 0))
assert Subs(f(x) * y, (x, y), (0, 1)) == Subs(f(y) * x, (y, x), (0, 1))
assert Subs(f(x) * y, (x, y), (1, 1)) == Subs(f(y) * x, (x, y), (1, 1))
assert Subs(f(x), x, 0).subs(x, 1).doit() == f(0)
assert Subs(f(x), x, y).subs(y, 0) == Subs(f(x), x, 0)
assert Subs(y * f(x), x, y).subs(y, 2) == Subs(2 * f(x), x, 2)
assert (2 * Subs(f(x), x, 0)).subs(Subs(f(x), x, 0), y) == 2 * y
assert Subs(f(x), x, 0).free_symbols == set()
assert Subs(f(x, y), x, z).free_symbols == {y, z}
assert Subs(f(x).diff(x), x, 0).doit(), Subs(f(x).diff(x), x, 0)
assert Subs(1 + f(x).diff(x), x, 0).doit(), 1 + Subs(f(x).diff(x), x, 0)
assert Subs(y*f(x, y).diff(x), (x, y), (0, 2)).doit() == \
2*Subs(Derivative(f(x, 2), x), x, 0)
assert Subs(y**2 * f(x), x, 0).diff(y) == 2 * y * f(0)
e = Subs(y**2 * f(x), x, y)
assert e.diff(y) == e.doit().diff(
y) == y**2 * Derivative(f(y), y) + 2 * y * f(y)
assert Subs(f(x), x, 0) + Subs(f(x), x, 0) == 2 * Subs(f(x), x, 0)
e1 = Subs(z * f(x), x, 1)
e2 = Subs(z * f(y), y, 1)
assert e1 + e2 == 2 * e1
assert e1.__hash__() == e2.__hash__()
assert Subs(z * f(x + 1), x, 1) not in [e1, e2]
assert Derivative(f(x), x).subs(x, g(x)) == Subs(Derivative(f(x), x),
(x, ), (g(x), ))
assert Subs(f(x)*cos(y) + z, (x, y), (0, pi/3)).n(2) == \
Subs(f(x)*cos(y) + z, (x, y), (0, pi/3)).evalf(2) == \
z + Rational('1/2').n(2)*f(0)
assert f(x).diff(x).subs(x, 0).subs(x, y) == f(x).diff(x).subs(x, 0)
assert (x * f(x).diff(x).subs(x, 0)).subs(
x, y) == y * f(x).diff(x).subs(x, 0)
def test_Subs():
assert Subs(x, (x, 0)) == Subs(y, (y, 0))
assert Subs(x, (x, 0)).subs({x: 1}) == Subs(x, (x, 0))
assert Subs(y, (x, 0)).subs({y: 1}) == Subs(1, (x, 0))
assert Subs(f(x), (x, 0)).doit() == f(0)
assert Subs(f(x**2), (x**2, 0)).doit() == f(0)
assert Subs(f(x, y, z), (x, 0), (y, 1), (z, 1)) != \
Subs(f(x, y, z), (x, 0), (y, 0), (z, 1))
assert Subs(f(x, y), (x, 0), (y, 1), (z, 1)) == \
Subs(f(x, y), (x, 0), (y, 1), (z, 2))
assert Subs(f(x, y), (x, 0), (y, 1), (z, 1)) != \
Subs(f(x, y) + z, (x, 0), (y, 1), (z, 0))
assert Subs(f(x, y), (x, 0), (y, 1)).doit() == f(0, 1)
assert Subs(Subs(f(x, y), (x, 0)), (y, 1)).doit() == f(0, 1)
pytest.raises(ValueError, lambda: Subs(f(x, y), x))
pytest.raises(ValueError, lambda: Subs(f(x, y), (x, 0), (x, 0), (y, 1)))
assert len(Subs(f(x, y), (x, 0), (y, 1)).variables) == 2
assert Subs(f(x, y), (x, 0), (y, 1)).point == Tuple(0, 1)
assert Subs(f(x), (x, 0)) == Subs(f(y), (y, 0))
assert Subs(f(x, y), (x, 0), (y, 1)) == Subs(f(x, y), (y, 1), (x, 0))
assert Subs(f(x)*y, (x, 0), (y, 1)) == Subs(f(y)*x, (y, 0), (x, 1))
assert Subs(f(x)*y, (x, 1), (y, 1)) == Subs(f(y)*x, (x, 1), (y, 1))
assert Subs(f(x), (x, 0)).subs({x: 1}).doit() == f(0)
assert Subs(f(x), (x, y)).subs({y: 0}) == Subs(f(x), (x, 0))
assert Subs(y*f(x), (x, y)).subs({y: 2}) == Subs(2*f(x), (x, 2))
assert (2 * Subs(f(x), (x, 0))).subs({Subs(f(x), (x, 0)): y}) == 2*y
assert Subs(f(x), (x, 0)).free_symbols == set()
assert Subs(f(x, y), (x, z)).free_symbols == {y, z}
assert Subs(f(x).diff(x), (x, 0)).doit(), Subs(f(x).diff(x), (x, 0))
assert Subs(1 + f(x).diff(x), (x, 0)).doit(), 1 + Subs(f(x).diff(x), (x, 0))
assert Subs(y*f(x, y).diff(x), (x, 0), (y, 2)).doit() == \
2*Subs(Derivative(f(x, 2), x), (x, 0))
assert Subs(y**2*f(x), (x, 0)).diff(y) == 2*y*f(0)
e = Subs(y**2*f(x), (x, y))
assert e.diff(y) == e.doit().diff(y) == y**2*Derivative(f(y), y) + 2*y*f(y)
assert Subs(f(x), (x, 0)) + Subs(f(x), (x, 0)) == 2*Subs(f(x), (x, 0))
e1 = Subs(z*f(x), (x, 1))
e2 = Subs(z*f(y), (y, 1))
assert e1 + e2 == 2*e1
assert e1.__hash__() == e2.__hash__()
assert Subs(z*f(x + 1), (x, 1)) not in (e1, e2)
assert Derivative(f(x), x).subs({x: g(x)}) == Derivative(f(g(x)), g(x))
assert Derivative(f(x), x).subs({x: x + y}) == Subs(Derivative(f(x), x),
(x, x + y))
assert Subs(f(x)*cos(y) + z, (x, 0), (y, pi/3)).evalf(2, strict=False) == \
Subs(f(x)*cos(y) + z, (x, 0), (y, pi/3)).evalf(2, strict=False) == \
z + Rational('1/2').evalf(2)*f(0)
assert f(x).diff(x).subs({x: 0}).subs({x: y}) == f(x).diff(x).subs({x: 0})
assert (x*f(x).diff(x).subs({x: 0})).subs({x: y}) == y*f(x).diff(x).subs({x: 0})
def test_Subs():
assert Subs(x, (x, 0)) == Subs(y, (y, 0))
assert Subs(x, (x, 0)).subs({x: 1}) == Subs(x, (x, 0))
assert Subs(y, (x, 0)).subs({y: 1}) == Subs(1, (x, 0))
assert Subs(f(x), (x, 0)).doit() == f(0)
assert Subs(f(x**2), (x**2, 0)).doit() == f(0)
assert Subs(f(x, y, z), (x, 0), (y, 1), (z, 1)) != \
Subs(f(x, y, z), (x, 0), (y, 0), (z, 1))
assert Subs(f(x, y), (x, 0), (y, 1), (z, 1)) == \
Subs(f(x, y), (x, 0), (y, 1), (z, 2))
assert Subs(f(x, y), (x, 0), (y, 1), (z, 1)) != \
Subs(f(x, y) + z, (x, 0), (y, 1), (z, 0))
assert Subs(f(x, y), (x, 0), (y, 1)).doit() == f(0, 1)
assert Subs(Subs(f(x, y), (x, 0)), (y, 1)).doit() == f(0, 1)
pytest.raises(ValueError, lambda: Subs(f(x, y), x))
pytest.raises(ValueError, lambda: Subs(f(x, y), (x, 0), (x, 0), (y, 1)))
assert len(Subs(f(x, y), (x, 0), (y, 1)).variables) == 2
assert Subs(f(x, y), (x, 0), (y, 1)).point == Tuple(0, 1)
assert Subs(f(x), (x, 0)) == Subs(f(y), (y, 0))
assert Subs(f(x, y), (x, 0), (y, 1)) == Subs(f(x, y), (y, 1), (x, 0))
assert Subs(f(x)*y, (x, 0), (y, 1)) == Subs(f(y)*x, (y, 0), (x, 1))
assert Subs(f(x)*y, (x, 1), (y, 1)) == Subs(f(y)*x, (x, 1), (y, 1))
assert Subs(f(x), (x, 0)).subs({x: 1}).doit() == f(0)
assert Subs(f(x), (x, y)).subs({y: 0}) == Subs(f(x), (x, 0))
assert Subs(y*f(x), (x, y)).subs({y: 2}) == Subs(2*f(x), (x, 2))
assert (2 * Subs(f(x), (x, 0))).subs({Subs(f(x), (x, 0)): y}) == 2*y
assert Subs(f(x), (x, 0)).free_symbols == set()
assert Subs(f(x, y), (x, z)).free_symbols == {y, z}
assert Subs(f(x).diff(x), (x, 0)).doit(), Subs(f(x).diff(x), (x, 0))
assert Subs(1 + f(x).diff(x), (x, 0)).doit(), 1 + Subs(f(x).diff(x), (x, 0))
assert Subs(y*f(x, y).diff(x), (x, 0), (y, 2)).doit() == \
2*Subs(Derivative(f(x, 2), x), (x, 0))
assert Subs(y**2*f(x), (x, 0)).diff(y) == 2*y*f(0)
e = Subs(y**2*f(x), (x, y))
assert e.diff(y) == e.doit().diff(y) == y**2*Derivative(f(y), y) + 2*y*f(y)
assert Subs(f(x), (x, 0)) + Subs(f(x), (x, 0)) == 2*Subs(f(x), (x, 0))
e1 = Subs(z*f(x), (x, 1))
e2 = Subs(z*f(y), (y, 1))
assert e1 + e2 == 2*e1
assert e1.__hash__() == e2.__hash__()
assert Subs(z*f(x + 1), (x, 1)) not in (e1, e2)
assert Derivative(f(x), x).subs({x: g(x)}) == Derivative(f(g(x)), g(x))
assert Derivative(f(x), x).subs({x: x + y}) == Subs(Derivative(f(x), x),
(x, x + y))
assert Subs(f(x)*cos(y) + z, (x, 0), (y, pi/3)).evalf(2, strict=False) == \
Subs(f(x)*cos(y) + z, (x, 0), (y, pi/3)).evalf(2, strict=False) == \
z + Rational('1/2').evalf(2)*f(0)
assert f(x).diff(x).subs({x: 0}).subs({x: y}) == f(x).diff(x).subs({x: 0})
assert (x*f(x).diff(x).subs({x: 0})).subs({x: y}) == y*f(x).diff(x).subs({x: 0})