def test_solve_from_derivative_roots(self):
epsilon = 0.00001
n_digits = convert_from_epsilon_to_n_digit(epsilon)
polynomial = parse_to_polynomial("x^3+x")
derivative_roots = []
roots = solve_from_derivative_roots(polynomial, epsilon,
derivative_roots)
expected_roots = [0]
for index in range(len(roots)):
self.assertEqual(round(roots[index], n_digits),
expected_roots[index])
polynomial = parse_to_polynomial("x^2-6*x+1")
derivative_roots = [3]
roots = solve_from_derivative_roots(polynomial, epsilon,
derivative_roots)
expected_roots = [0.1716, 5.8284]
for index in range(len(roots)):
self.assertEqual(round(roots[index], n_digits),
expected_roots[index])
polynomial = parse_to_polynomial("x^3-3*x^2+2*x-10")
derivative_roots = [0.42, 1.57]
roots = solve_from_derivative_roots(polynomial, epsilon,
derivative_roots)
expected_roots = [3.3089]
for index in range(len(roots)):
self.assertEqual(round(roots[index], n_digits),
expected_roots[index])
def test_get_upper_bound_with_opposite_sign(self):
self.assertEqual(
get_upper_bound_with_opposite_sign(parse_to_polynomial("x^3"), 1),
None)
self.assertEqual(
get_upper_bound_with_opposite_sign(parse_to_polynomial("x^3"),
-10), 5)
def test_get_lower_bound_with_opposite_sign(self):
self.assertEqual(
get_lower_bound_with_opposite_sign(parse_to_polynomial("x^3"), 1),
0)
self.assertEqual(
get_lower_bound_with_opposite_sign(parse_to_polynomial("x^2+9"),
-2), None)
def test_bisect(self):
epsilon = 0.00001
n_digits = convert_from_epsilon_to_n_digit(epsilon)
polynomial = parse_to_polynomial("x^3/3-x")
root = find_root_using_bisection(polynomial, epsilon, 1, 10)
self.assertEqual(round(root, n_digits), 1.7321)
polynomial = parse_to_polynomial("x^2-x-2")
root = find_root_using_bisection(polynomial, epsilon, -100, 0)
self.assertEqual(round(root, n_digits), -1)
polynomial = parse_to_polynomial("x^2-x-2")
root = find_root_using_bisection(polynomial, epsilon, -100, -10)
self.assertEqual(root, None)
def parse_and_solve_and_round(expression, epsilon):
if expression.find("=") < 0:
roots = solve_equation(parse_to_polynomial(expression), epsilon)
else:
if expression.endswith("=0"):
roots = solve_equation(
parse_to_polynomial(expression[0:len(expression) - 2]),
epsilon)
else:
index_of_equal = expression.find("=")
a = parse_to_polynomial(expression[0:index_of_equal])
b = parse_to_polynomial(expression[index_of_equal + 1:])
roots = solve_equation(a.minus(b), epsilon)
if roots == ["Infinite roots"]:
return roots
n_digits = convert_from_epsilon_to_n_digit(epsilon)
return list(map(lambda root: round(root, n_digits), roots))
def test_solve_equation(self):
epsilon = 0.0001
polynomial = parse_to_polynomial("0*x+6")
roots = solve_equation(polynomial, epsilon)
self.assertEqual(roots, [])
polynomial = parse_to_polynomial("0*x+0")
roots = solve_equation(polynomial, epsilon)
self.assertEqual(roots, ["Infinite roots"])
polynomial = parse_to_polynomial("11*x+6")
roots = solve_equation(polynomial, epsilon)
expected_roots = [-6 / 11]
self.assertEqual(len(roots), len(expected_roots))
for index in range(len(roots)):
self.assertEqual(roots[index], expected_roots[index])
polynomial = parse_to_polynomial("6*x^2+11*x+6")
roots = solve_equation(polynomial, epsilon)
expected_roots = []
self.assertEqual(len(roots), len(expected_roots))
for index in range(len(roots)):
self.assertEqual(roots[index], expected_roots[index])
polynomial = parse_to_polynomial("x^3+6*x^2+11*x+6")
roots = solve_equation(polynomial, epsilon)
expected_roots = [-3, -2, -1]
self.assertEqual(len(roots), len(expected_roots))
for index in range(len(roots)):
self.assertEqual(roots[index], expected_roots[index])
polynomial = parse_to_polynomial("x^2-1").multiply(
parse_to_polynomial("x^2-4"))
roots = solve_equation(polynomial, epsilon)
expected_roots = [-2, -1, 1, 2]
self.assertEqual(len(roots), len(expected_roots))
for index in range(len(roots)):
self.assertEqual(roots[index], expected_roots[index])