Struct UnitalMagma 

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

A set equipped with a binary operation and a specified identity element.

UnitalMagma is a representation of the abstract algebraic unital magma. The existence of an identity element is all that is required of its binary operation. Its construction requires a set (specifically an AlgaeSet) and an identity-preserving BinaryOperation.

Examples

use algae_rs::algaeset::AlgaeSet;
use algae_rs::mapping::{BinaryOperation, IdentityOperation};
use algae_rs::magma::{Magmoid, UnitalMagma};

let mut add = IdentityOperation::new(&|a, b| a + b, 0);
let mut magma = UnitalMagma::new(
    AlgaeSet::<i32>::all(),
    &mut add,
    0
);

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

let mut bad_add = IdentityOperation::new(&|a, b| a + b, 3);
let mut bad_magma = UnitalMagma::new(
    AlgaeSet::<i32>::all(),
    &mut bad_add,
    3
);

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

Implementations

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

fn from(monoid: Monoid<'a, T>) -> UnitalMagma<'a, T>

Converts to this type from the input type.

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

fn from(magma: UnitalMagma<'a, T>) -> Magma<'a, T>

Converts to this type from the input type.

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

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

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