def test_derivative():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.diff(x) == function_symbol("f", x).diff(x)
assert f.diff(x).diff(x) == function_symbol("f", x).diff(x).diff(x)
assert f.diff(y) == 0
assert f.diff(x).args == (f, x)
assert f.diff(x).diff(x).args == (f, x, x)
g = function_symbol("f", y)
assert g.diff(x) == 0
assert g.diff(y) == function_symbol("f", y).diff(y)
assert g.diff(y).diff(y) == function_symbol("f", y).diff(y).diff(y)
assert f - function_symbol("f", x) == 0
f = function_symbol("f", x, y)
assert f.diff(x).diff(y) == function_symbol("f", x, y).diff(x).diff(y)
assert f.diff(Symbol("z")) == 0
s = Derivative(function_symbol("f", x), x)
assert s.expr == function_symbol("f", x)
assert s.variables == (x,)
fxy = Function("f")(x, y)
g = Derivative(Function("f")(x, y), x, 2, y, 1)
assert g == fxy.diff(x, x, y)
assert g == fxy.diff(y, 1, x, 2)
assert g == fxy.diff(y, x, 2)
def test_Subs():
x = Symbol("x")
y = Symbol("y")
_x = Symbol("_xi_1")
f = function_symbol("f", 2*x)
assert f.diff(x) == 2 * Subs(Derivative(function_symbol("f", _x), [_x]), [_x], [2 * x])
assert Subs(Derivative(function_symbol("f", x, y), [x]), [x, y], [_x, x]) \
== Subs(Derivative(function_symbol("f", x, y), [x]), [y, x], [x, _x])
def test_Subs():
x = Symbol("x")
y = Symbol("y")
_x = Symbol("_xi_1")
f = function_symbol("f", 2*x)
assert str(f.diff(x)) == "2*Subs(Derivative(f(_xi_1), _xi_1), (_xi_1), (2*x))"
# TODO: fix me
# assert f.diff(x) == 2 * Subs(Derivative(function_symbol("f", _x), _x), [_x], [2 * x])
assert Subs(Derivative(function_symbol("f", x, y), x), [x, y], [_x, x]) \
== Subs(Derivative(function_symbol("f", x, y), x), [y, x], [x, _x])
s = f.diff(x)/2
_xi_1 = Symbol("_xi_1")
assert s.expr == Derivative(function_symbol("f", _xi_1), _xi_1)
assert s.variables == (_xi_1,)
assert s.point == (2*x,)
def test_conv11():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
x1 = Symbol("x")
y1 = Symbol("y")
e1 = sympy.Subs(sympy.Derivative(sympy.Function("f")(x, y), x), [x, y],
[y, y])
e2 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [x1, y1],
[y1, y1])
e3 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [y1, x1],
[x1, y1])
assert sympify(e1) == e2
assert sympify(e1) != e3
assert e2._sympy_() == e1
assert e3._sympy_() != e1