Module permutation

A permutation is a bijection of a set. Together with function composition this forms a group.

Examples

A permutation is a GroupElement and can therefore be multiplied together. From the following computation it is clear that we compose from left to right.

use std::collections::HashMap;
use permutation_rs::group::GroupElement;
use permutation_rs::group::permutation::Permutation;

let mut left_image = HashMap::new();
left_image.insert(0, 1);
left_image.insert(1, 0);
left_image.insert(2, 2);
let left = Permutation::new(left_image);

let mut right_image = HashMap::new();
right_image.insert(0, 0);
right_image.insert(1, 2);
right_image.insert(2, 1);
let right = Permutation::new(right_image);

let answer = left.times(&right);

let mut expected_image = HashMap::new();
expected_image.insert(0, 2);
expected_image.insert(1, 0);
expected_image.insert(2, 1);
let expected = Permutation::new(expected_image);

assert_eq!(answer, expected);

Writing the above permutations can get a bit unwieldy. You can use the permute! macro to alleviate the tedium a bit. For example, the left permutation could have been written like this

let left = permute!(
    0, 1,
    1, 0,
    2, 2
);

Structs

Permutation

A permutation of the set 0..n for a suitable choice of n.