def test_x_eval_10(self):
self.assertEqual(X().eval(10), 10)
def test_x_is_expression(self):
self.assertIsInstance(X(), Expression)
def test_div_diff(self):
x = X()
f = Div(x, Add(Mul(x, x), Number(1))) # f(x) = x / (x**2 + 1)
self.assertAlmostEqual(f.diff().eval(1), 0)
self.assertAlmostEqual(f.diff().eval(2), -3 / 25)
def test_sub_diff(self):
x = X()
f = Sub(Mul(x, x), Mul(Number(2), x)) # f(x) = x**2 - 2x
self.assertEqual(f.diff().eval(2), 2)
def test_div(self):
x = X()
f = Div(x, Add(Mul(x, x), Number(1))) # f(x) = x / (x**2 + 1)
self.assertAlmostEqual(f.eval(2), 0.4)
def test_xx_3x_2_diff(self):
x = X()
f = Add(Add(Mul(x, x), Mul(Number(3), x)), Number(2))
# f(x) = x**2 + 3x + 2
self.assertEqual(f.diff().eval(10), 23)
def test_2x_3_diff(self):
f = Add(Mul(Number(2), X()), Number(3)) # f(x) = 2x + 3
self.assertEqual(f.diff().eval(100), 2)
def test_2x_3_eval(self):
f = Add(Mul(Number(2), X()), Number(3)) # f(x) = 2x + 3
self.assertEqual(f.eval(10), 23)
def test_x_diff(self):
self.assertEqual(X().diff().eval(0), 1)
def test_x_diff_is_a_number(self):
self.assertIsInstance(X().diff(), Number)