Trait Group 

pub trait Group: Monoid {
    // Required method
    fn inverse(&self) -> Self;
}

A group: a monoid where every element has an inverse.

Laws (not enforced by type system):

• Associative: a.combine(b).combine(c) == a.combine(b.combine(c))
• Identity: a.combine(empty()) == a == empty().combine(a)
• Inverse: a.combine(a.inverse()) == empty() == a.inverse().combine(a)

Example

use algebra::Group;
use algebra::Monoid;
use algebra::Semigroup;

#[derive(Clone, Copy, Debug, PartialEq, Eq)]
struct AddInt(i32);

impl Semigroup for AddInt {
    fn combine(&self, other: &Self) -> Self {
        AddInt(self.0 + other.0)
    }
}

impl Monoid for AddInt {
    fn empty() -> Self {
        AddInt(0)
    }
}

impl Group for AddInt {
    fn inverse(&self) -> Self {
        AddInt(-self.0)
    }
}

let x = AddInt(5);
let inv = x.inverse();
assert_eq!(x.combine(&inv), AddInt::empty());

Required Methods

fn inverse(&self) -> Self

Return the inverse of this element.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors