Trait Semiring 

pub trait Semiring:
    Copy
    + Clone
    + Send
    + Sync
    + 'static {
    type Scalar: Scalar;

    // Required methods
    fn zero() -> Self;
    fn one() -> Self;
    fn add(self, rhs: Self) -> Self;
    fn mul(self, rhs: Self) -> Self;
    fn from_scalar(s: Self::Scalar) -> Self;
    fn to_scalar(self) -> Self::Scalar;
    fn is_zero(&self) -> bool;
}

A semiring defines two binary operations (⊕, ⊗) with identities.

Semiring Laws

For a semiring (S, ⊕, ⊗, 0, 1):

• (S, ⊕, 0) is a commutative monoid
• (S, ⊗, 1) is a monoid
• ⊗ distributes over ⊕
• 0 annihilates: a ⊗ 0 = 0 ⊗ a = 0

Examples

Semiring	⊕	⊗	0	1
Standard	+	×	0	1
MaxPlus	max	+	-∞	0
MinPlus	min	+	+∞	0
MaxMul	max	×	0	1

Required Associated Types

type Scalar: Scalar

The underlying scalar type

Required Methods

fn zero() -> Self

Additive identity (zero element for ⊕)

fn one() -> Self

Multiplicative identity (one element for ⊗)

fn add(self, rhs: Self) -> Self

Addition operation (⊕)

fn mul(self, rhs: Self) -> Self

Multiplication operation (⊗)

fn from_scalar(s: Self::Scalar) -> Self

Create from scalar value

fn to_scalar(self) -> Self::Scalar

Extract scalar value

fn is_zero(&self) -> bool

Check if this is the zero 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

impl<T: Scalar + Zero + One + PartialEq + Add<Output = T> + Mul<Output = T>> Semiring for Standard<T>

type Scalar = T