def test_split(self):
# If this ever breaks, we should solve the problem by writing a
# new kind of Function that turns a lambda expression into a
# Function. That way, it will never be simplified.
# f = x^2 + x
f = Function.sum(Function.power(Function.identity(),
Function.constant(2)),
Function.identity())
# f(-1) = 0, f(0) = 0, f(-.5) = -.25
# The range of f on [-1,0] is [-.25,0]
# f([-1,0]) = [-1,1]
# f([-1,-.5]) = [-.75,.5]
# f([-.5,0]) = [-.5,.25]
# This will never finish, since it asks for the exact bounds
self.assertTrue(is_bounded(f, Interval(-1,0), Interval(-1/4,0))
is None)
# g = 1/2*x^3-3/2*x
g = Function.sum(Function.product(
Function.constant(.5),
Function.power(Function.identity(),
Function.constant(3))),
Function.product(Function.constant(-1.5),
Function.identity()))
self.assertEqual(is_bounded(g, Interval(-1.5,1.5), Interval(-.9,1)),
False)
# This encounters a ValueError on the first split so should
# return None
h = Function.quotient(Function.constant(1), Function.identity())
self.assertTrue(is_bounded(h, Interval(-1,1), Interval(-5,5)) is None)
