Lenstra-Lenstra-Lovász (LLL) reduction

Transforms a lattice's basis into a form in which the first vector of the basis is not "much" longer than the shortest (non-zero) vector of the lattice:

||first basis vector|| <= 2^((n-1)/2) ||shortest vector||

where n is the dimension of lattice (assuming LOVASZ_FACTOR = 4.0/3.0).

LLL Reduction at Wikipedia

Usage

use lllreduce::{
		Basetype, 
        gram_schmidt_with_coeffs, 
        lll_reduce};

fn main() {
	let original_mtx : std::vec::Vec<std::vec::Vec::<Basetype>> = vec![
		vec![0.0,3.0,4.0,7.0,8.0],
		vec![1.0,0.0,1.0,8.0,7.0],
		vec![1.0,1.0,3.0,5.0,6.0],
		vec![0.0,3.0,4.0,7.0,6.0],
		vec![0.0,3.0,4.0,8.0,9.0]
	];
    let mut mtxtuple = lllreduce::gram_schmidt_with_coeffs(original_mtx);
	lll_reduce(&mut mtxtuple);
    println!("\tLLL-reduced basis");
    for a in &mtxtuple.2 {
        println!("\t\t{:?}", a);
    }    
    println!("\tumtx");
    for a in &mtxtuple.0 {
        println!("\t\t{:?}", a);
    }
    println!("\tqmtx");
    for a in &mtxtuple.1 {
        println!("\t\t{:?}", a);
    }
}

Note

This is the very first, very drafty version, anything can change in it in the future.