def test_constant_equality(self):
"""Test that Constant(1) is equal to other instances of 1."""
to_test = [Polynomial(1), Monomial(1, 0), Constant(1), 1]
for val in to_test:
self.assertEqual(Constant(1), val)
def test_calculate_zero_polynomial(self):
"""Test that calculations of zero polynomial values always give 0."""
self.assertEqual(0, ZeroPolynomial().calculate(1))
self.assertEqual(0, Constant(0).calculate(5))
self.assertEqual(0, Monomial(0, 1).calculate(1.1))
def test_monomial_vector(self):
"""Test _vector for Monomials."""
m = Monomial(6, 5)
self.assertEqual([0, 0, 0, 0, 0, 6], m._vector)
m._vector = [0, 0, 0, 0]
self.assertEqual(0, m.coefficient)
def test_monomial_set_degree(self):
"""Test setting Monomial degree"""
m = Monomial(6, 5)
self.assertEqual(5, m.degree)
m.degree = 4
self.assertEqual(4, m.degree)
def get_cycle_index_sym(n: int) -> Polynomial:
"""
Compute the cycle index
of S_n, i.e. the symmetry
group of n symbols.
"""
if n < 0:
raise ValueError("n should be a non-negative integer.")
memo = {
0:
Polynomial([Monomial({}, Fraction(1, 1))]),
1:
Polynomial([Monomial({1: 1}, Fraction(1, 1))]),
2:
Polynomial([
Monomial({1: 2}, Fraction(1, 2)),
Monomial({2: 1}, Fraction(1, 2))
]),
3:
Polynomial([
Monomial({1: 3}, Fraction(1, 6)),
Monomial({
1: 1,
2: 1
}, Fraction(1, 2)),
Monomial({3: 1}, Fraction(1, 3)),
]),
4:
Polynomial([
Monomial({1: 4}, Fraction(1, 24)),
Monomial({
2: 1,
1: 2
}, Fraction(1, 4)),
Monomial({
3: 1,
1: 1
}, Fraction(1, 3)),
Monomial({2: 2}, Fraction(1, 8)),
Monomial({4: 1}, Fraction(1, 4)),
]),
}
result = cycle_index_sym_helper(n, memo)
return result