This test program runs find_roots_sturm to determine the real roots of the quartic polynomial x^4 - 7x^3 + 7x - 1.
fn main() {
println!(
"{:?}",
roots::find_roots_sturm(&[-7.0, 0.0, 7.0, -1.0], &mut 1.0e-12)
);
}As of roots v0.0.8, this is its output, which is incorrect:
[Ok(-1.0000000000000007), Ok(0.145898033750315), Ok(1.0000000000000009)]
This quartic happens to factorise as (x - 1) (x + 1) (x^2 - 7x + 1), and therefore its roots are +1, -1, and by the quadratic formula (7 ± √45) / 2, i.e. about 0.145898 and 6.854102. So find_roots_sturm has missed the large root 6.854102, and returned only the other three.
More generally, no real quartic has three real roots! If it has complex roots, then they appear in conjugate pairs, so there can be 0, 2 or 4 real roots, but not 1 or 3. So even without being able to factorise this quartic, it's clear that an answer of length 3 is wrong.
This test program runs
find_roots_sturmto determine the real roots of the quartic polynomialx^4 - 7x^3 + 7x - 1.As of
rootsv0.0.8, this is its output, which is incorrect:This quartic happens to factorise as
(x - 1) (x + 1) (x^2 - 7x + 1), and therefore its roots are +1, -1, and by the quadratic formula (7 ± √45) / 2, i.e. about 0.145898 and 6.854102. Sofind_roots_sturmhas missed the large root 6.854102, and returned only the other three.More generally, no real quartic has three real roots! If it has complex roots, then they appear in conjugate pairs, so there can be 0, 2 or 4 real roots, but not 1 or 3. So even without being able to factorise this quartic, it's clear that an answer of length 3 is wrong.