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})