Function find_real_roots_of_polynomial::bisection_method

pub fn bisection_method<K>(
    f: &Polynomial<K>, 
    limit: &K, 
    left: K, 
    right: K
) -> (K, K) where
    K: Sized + Clone + Ord + Zero + One + for<'x> AddAssign<&'x K> + for<'x> MulAssign<&'x K>,
    for<'x> &'x K: Add<Output = K> + Sub<Output = K> + Mul<Output = K> + Div<Output = K>, 

Find root of f from (left, right] by bisection method.

Require: f has exact one solution on (left, right]. Iteration stops if right - left < limit.

use find_real_roots_of_polynomial::bisection_method;
use polynomial_ring::{polynomial, Polynomial};
use num::{BigRational, BigInt};
let v = [-2, 0, 1].iter().map(|x| BigRational::from(BigInt::from(*x))).collect::<Vec<_>>();
let f = Polynomial::new(v); // f=x^2-2
let limit = BigRational::new(BigInt::from(1), BigInt::from(10)); // 1/10
let left = BigRational::from(BigInt::from(0));
let right = BigRational::from(BigInt::from(2));
// (left, right] = (0, 2]
let (l, r) = bisection_method::<BigRational>(&f, &limit, left, right);
assert!(&r - &l < limit);
assert_eq!(l, BigRational::new(BigInt::from(11), BigInt::from(8))); // 11/8 = 1.375
assert_eq!(r, BigRational::new(BigInt::from(23), BigInt::from(16))); // 23/16 = 1.4375