Trait un_algebra::monoid::mul_monoid::MulMonoid

pub trait MulMonoid: MulSemigroup {
    fn one() -> Self;

    fn is_one(&self) -> bool { ... }
    fn axiom_left_mul_identity(&self) -> bool { ... }
    fn axiom_right_mul_identity(&self) -> bool { ... }
}

An algebraic multiplicative monoid.

Required Methods

fn one() -> Self

Unique one (multiplicative identity) element. One is ideally a const value, but the const rules make it too difficult to create const instances for many third party types.

Provided Methods

fn is_one(&self) -> bool

Test for the one (multiplicative identity) element.

fn axiom_left_mul_identity(&self) -> bool

Test the left multiplicative identity axiom.

fn axiom_right_mul_identity(&self) -> bool

Test the right multiplicative identity axiom.

Implementations on Foreign Types

impl MulMonoid for u8

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for u16

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for u32

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for u64

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for u128

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for usize

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for i8

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for i16

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for i32

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for i64

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for i128

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for isize

fn one() -> Self

One is just integer one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

impl MulMonoid for BigRational

Rational numbers form a multiplicative monoid.

fn one() -> Self

One is rational one.

fn is_one(&self) -> bool

fn axiom_left_mul_identity(&self) -> bool

fn axiom_right_mul_identity(&self) -> bool

Implementors