def test_delta_derivative(self):
exp, x, d = tree('x ^ 2, x, d')
self.assertEqual(tree('d/dx x ^ 2'), der(exp, x))
self.assertEqual(tree('d / dx x ^ 2'), der(exp, x))
self.assertEqual(tree('d/dx x ^ 2 + x'), der(exp, x) + x)
self.assertEqual(tree('d/dx (x ^ 2 + x)'), der(exp + x, x))
self.assertEqual(tree('d/d'), d / d)
def test_derivative(self):
x = tree('x')
self.assertEqual(tree('[x]\''), der(x))
self.assertEqual(tree('x\''), der(x))
self.assertEqual(tree('[x]\'\''), der(der(x)))
self.assertEqual(tree('(x)\'\''), der(der(x)))
self.assertEqual(tree('x\'\''), der(der(x)))
def test_product_rule(self):
root = tree('(x ^ 2 * x)\'')
x2, x = f = root[0]
self.assertEqual(product_rule(root, (Scope(f), x2)),
der(x2) * x + x2 * der(x))
self.assertEqual(product_rule(root, (Scope(f), x)),
der(x) * x2 + x * der(x2))
root = tree('(x ^ 2 * x * x ^ 3)\'')
(x2, x), x3 = f = root[0]
self.assertEqual(product_rule(root, (Scope(f), x2)),
der(x2) * (x * x3) + x2 * der(x * x3))
self.assertEqual(product_rule(root, (Scope(f), x)),
der(x) * (x2 * x3) + x * der(x2 * x3))
self.assertEqual(product_rule(root, (Scope(f), x3)),
der(x3) * (x2 * x) + x3 * der(x2 * x))
def test_const_deriv_multiplication(self):
root = tree('d/dx 2x')
l2, x = root[0]
args = Scope(root[0]), l2, x
self.assertEqual(const_deriv_multiplication(root, args),
l2 * der(x, x))
self.assertRewrite(["[2x]'", "2[x]'", '2 * 1', '2'])
def test_sum_rule(self):
root = tree('(x ^ 2 + x)\'')
x2, x = f = root[0]
self.assertEqual(sum_rule(root, (Scope(f), x2)), der(x2) + der(x))
self.assertEqual(sum_rule(root, (Scope(f), x)), der(x) + der(x2))
root = tree('(x ^ 2 + 3 + x)\'')
(x2, l3), x = f = root[0]
self.assertEqual(sum_rule(root, (Scope(f), x2)), der(x2) + der(l3 + x))
self.assertEqual(sum_rule(root, (Scope(f), x)), der(x) + der(x2 + l3))
def test_der(self):
x2, x, y = tree('x ^ 2, x, y')
self.assertEqual(der(x2), tree('[x ^ 2]\''))
self.assertEqual(der(x2, x), tree('d/dx x ^ 2'))
self.assertEqual(der(x2, y), tree('d/dy x ^ 2'))
def test_quotient_rule(self):
root = tree('(x ^ 2 / x)\'')
f, g = root[0]
self.assertEqual(quotient_rule(root, ()),
(der(f) * g - f * der(g)) / g ** 2)
def test_tangens(self):
root, x = tree('d/dx tan(x), x')
self.assertEqual(tangens(root, ()), der(sin(x) / cos(x), x))
root = tree('tan(x)\'')
self.assertEqual(tangens(root, ()), der(sin(x) / cos(x)))
def test_chain_rule(self):
root = tree('(2 ^ x ^ 3)\'')
l2, x3 = root[0]
x, l3 = x3
self.assertEqual(chain_rule(root, (x3, variable_exponent, ())),
l2 ** x3 * ln(l2) * der(x3))