Struct algae_rs::magma::Group

pub struct Group<'a, T> { /* private fields */ }

A monoid with inverses.

Group is a representation of the abstract algebraic group. Associativity, invertibility, and identity preservation are all required of its binary operation. Its construction involves a set (specifically an AlgaeSet) and a BinaryOperation with the aforementioned properties.

Examples

use algae_rs::algaeset::AlgaeSet;
use algae_rs::mapping::{BinaryOperation, GroupOperation};
use algae_rs::magma::{Magmoid, Group};

let mut add = GroupOperation::new(&|a, b| a + b, &|a, b| a - b, 0);
let mut group = Group::new(AlgaeSet::<i32>::all(), &mut add, 0);

let sum = group.with(1, 2);
assert!(sum.is_ok());
assert!(sum.unwrap() == 3);

let difference = group.with(1, -1);
assert!(difference.is_ok());
assert!(difference.unwrap() == 0);

let mut bad_add = GroupOperation::new(&|a, b| a + b, &|a, b| a * b, 0);
let mut bad_group = Group::new(AlgaeSet::<i32>::all(), &mut bad_add, 0);

let bad_sum = bad_group.with(3, 2);
assert!(bad_sum.is_err());

let bad_difference = bad_group.with(1, -1);
assert!(bad_difference.is_err());

Implementations

impl<'a, T: Copy + PartialEq> Group<'a, T>

pub fn new(
aset: AlgaeSet<T>,
binop: &'a mut dyn BinaryOperation<T>,
identity: T
) -> Self

Trait Implementations

impl<'a, T> From<Group<'a, T>> for Magma<'a, T>

fn from(group: Group<'a, T>) -> Magma<'a, T>

Converts to this type from the input type.

impl<'a, T: Copy + PartialEq> From<Group<'a, T>> for Quasigroup<'a, T>

fn from(group: Group<'a, T>) -> Quasigroup<'a, T>

Converts to this type from the input type.

impl<'a, T: Copy + PartialEq> From<Group<'a, T>> for UnitalMagma<'a, T>

fn from(group: Group<'a, T>) -> UnitalMagma<'a, T>

Converts to this type from the input type.

impl<'a, T: Copy + PartialEq> Magmoid<T> for Group<'a, T>

fn binop(&mut self) -> &mut dyn BinaryOperation<T>

fn with(&mut self, left: T, right: T) -> Result<T, PropertyError>