def test_trig_func_class_stuff():
for name, func in [('sin', sin), ('cos', cos), ('tan', tan)]:
assert func(2 * x).arg == 2 * x
with pytest.raises(TypeError):
func(x, y)
assert repr(func(x)) == name + '(x)'
assert func(f(x)).replace(f(x), y) == func(y) # test apply_to_content
assert func(x).pow_parenthesize() == '(%s(x))' % name
def test_trig_derivatives():
assert sin(x).derivative(x) == cos(x)
assert cos(x).derivative(x) == -sin(x)
assert tan(x).derivative(x) == 1 + tan(x)**2
assert sin(f(x)).derivative(x) == cos(f(x)) * f_(x)
assert cos(f(x)).derivative(x) == -sin(f(x)) * f_(x)
assert tan(f(x)).derivative(x) == f_(x) + f_(x) * tan(f(x))**2
def test_eqs_and_hashes(hasheq):
assert hasheq(x, x)
assert not hasheq(x, y)
assert hasheq(f(x), f(x))
assert hasheq(f_(x), f_(x))
assert not hasheq(f(x), f(y))
assert not hasheq(f(x), f_(x))
assert not hasheq(f(x), g(x))
def test_derivatives():
with pytest.raises(ValueError,
match="negative derivative_count is not supported$"):
f(x, derivative_count=-1)
assert x.derivative(x) == mathify(1)
assert x.derivative(y) == mathify(0)
assert f(x).derivative(x) == f_(x)
assert f(x).derivative(x).derivative(x) == f__(x)
assert f(x).derivative(y) == mathify(0)
assert f(
g(x)).derivative(x) == f_(g(x)) * g_(x), "u forgot chain rule n00b"
def test_derivatives():
assert (f(x) + g(x) + h(x)).derivative(x) == f_(x) + g_(x) + h_(x)
assert (f(x) * g(x) *
h(x)).derivative(x) == (f_(x) * g(x) * h(x) + f(x) * g_(x) * h(x) +
f(x) * g(x) * h_(x))
assert (f(x)**g(x)).derivative(x) == (
f(x)**g(x) * (g_(x) * ln(f(x)) + g(x) * f_(x) / f(x)))
assert (f(x)**a).derivative(x) == a * f(x)**(a - 1) * f_(x)
assert (a**f(x)).derivative(x) == a**f(x) * ln(a) * f_(x)
def test_reprs():
assert repr(x) == 'x'
assert repr(f(x)) == 'f(x)'
assert repr(f(x, derivative_count=2)) == "f''(x)"
def test_automagic_mathify():
assert f(2).arg == mathify(2)
def test_may_depend_on():
assert x.may_depend_on(x)
assert not x.may_depend_on(y)
assert f(x).may_depend_on(x)
assert not f(x).may_depend_on(y)