def test_cyclotomic_poly():
pytest.raises(ValueError, lambda: cyclotomic_poly(0, x))
assert cyclotomic_poly(1, x, polys=True) == Poly(x - 1)
assert cyclotomic_poly(1, polys=True) == Poly(x - 1)
assert cyclotomic_poly(1, x) == x - 1
assert cyclotomic_poly(2, x) == x + 1
assert cyclotomic_poly(3, x) == x**2 + x + 1
assert cyclotomic_poly(4, x) == x**2 + 1
assert cyclotomic_poly(5, x) == x**4 + x**3 + x**2 + x + 1
assert cyclotomic_poly(6, x) == x**2 - x + 1
def test_roots_cyclotomic():
assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True)) == [1]
assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True)) == [-1]
assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True)) == [
-Rational(1, 2) - I * sqrt(3) / 2, -Rational(1, 2) + I * sqrt(3) / 2
]
assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True)) == [-I, I]
assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True)) == [
Rational(1, 2) - I * sqrt(3) / 2,
Rational(1, 2) + I * sqrt(3) / 2
]
assert roots_cyclotomic(cyclotomic_poly(7, x, polys=True)) == [
-cos(pi / 7) - I * sin(pi / 7),
-cos(pi / 7) + I * sin(pi / 7),
-cos(3 * pi / 7) - I * sin(3 * pi / 7),
-cos(3 * pi / 7) + I * sin(3 * pi / 7),
cos(2 * pi / 7) - I * sin(2 * pi / 7),
cos(2 * pi / 7) + I * sin(2 * pi / 7),
]
assert roots_cyclotomic(cyclotomic_poly(8, x, polys=True)) == [
-sqrt(2) / 2 - I * sqrt(2) / 2,
-sqrt(2) / 2 + I * sqrt(2) / 2,
sqrt(2) / 2 - I * sqrt(2) / 2,
sqrt(2) / 2 + I * sqrt(2) / 2,
]
assert roots_cyclotomic(cyclotomic_poly(12, x, polys=True)) == [
-sqrt(3) / 2 - I / 2,
-sqrt(3) / 2 + I / 2,
sqrt(3) / 2 - I / 2,
sqrt(3) / 2 + I / 2,
]
assert roots_cyclotomic(cyclotomic_poly(1, x, polys=True),
factor=True) == [1]
assert roots_cyclotomic(cyclotomic_poly(2, x, polys=True),
factor=True) == [-1]
assert roots_cyclotomic(cyclotomic_poly(3, x, polys=True), factor=True) == \
[-root(-1, 3), -1 + root(-1, 3)]
assert roots_cyclotomic(cyclotomic_poly(4, x, polys=True), factor=True) == \
[-I, I]
assert roots_cyclotomic(cyclotomic_poly(5, x, polys=True), factor=True) == \
[-root(-1, 5), -root(-1, 5)**3, root(-1, 5)**2, -1 - root(-1, 5)**2 + root(-1, 5) + root(-1, 5)**3]
assert roots_cyclotomic(cyclotomic_poly(6, x, polys=True), factor=True) == \
[1 - root(-1, 3), root(-1, 3)]