Struct algae_rs::magma::Loop

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

A quasigroup with identity

Loop is a representation of the abstract algebraic loop. Cancellativity (ie. the Latin Square property) and identity preservation are both 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, LoopOperation};
use algae_rs::magma::{Magmoid, Loop};

let mut add = LoopOperation::new(&|a, b| a + b, 0);
let mut quasigroup = Loop::new(
    AlgaeSet::<i32>::all(),
    &mut add,
    0
);
let sum = quasigroup.with(1, 2);
assert!(sum.is_ok());
assert!(sum.unwrap() == 3);

Implementations

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

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

Trait Implementations

impl<'a, T: Copy + PartialEq> From<Loop<'a, T>> for Magma<'a, T>

fn from(loop_: Loop<'a, T>) -> Magma<'a, T>

Converts to this type from the input type.

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

fn from(loop_: Loop<'a, T>) -> Quasigroup<'a, T>

Converts to this type from the input type.

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

fn from(loop_: Loop<'a, T>) -> UnitalMagma<'a, T>

Converts to this type from the input type.

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

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

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