Trait alga::general::AbstractRing

pub trait AbstractRing<A: Operator = Additive, M: Operator = Multiplicative>: AbstractGroupAbelian<A> + AbstractMonoid<M> {
    // Provided methods
    fn prop_mul_and_add_are_distributive_approx(
        args: (Self, Self, Self)
    ) -> bool
       where Self: RelativeEq { ... }
    fn prop_mul_and_add_are_distributive(args: (Self, Self, Self)) -> bool
       where Self: Eq { ... }
}

A ring is the combination of an Abelian group and a multiplicative monoid structure.

A ring is equipped with:

• An abstract operator (usually the addition, “+”) that fulfills the constraints of an Abelian group.

  An Abelian group is a set with a closed commutative and associative addition with the divisibility property and an identity element.

• A second abstract operator (usually the multiplication, “×”) that fulfills the constraints of a monoid.

  A set equipped with a closed associative multiplication with the divisibility property and an identity element.

The multiplication is distributive over the addition:

Distributivity

a, b, c ∈ Self, a × (b + c) = a × b + a × c.

Provided Methods

fn prop_mul_and_add_are_distributive_approx(args: (Self, Self, Self)) -> bool

where Self: RelativeEq,

Returns true if the multiplication and addition operators are distributive for the given argument tuple. Approximate equality is used for verifications.

fn prop_mul_and_add_are_distributive(args: (Self, Self, Self)) -> bool

where Self: Eq,

Returns true if the multiplication and addition operators are distributive for the given argument tuple.

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl AbstractRing for f32

impl AbstractRing for f64

impl AbstractRing for i8

impl AbstractRing for i16

impl AbstractRing for i32

impl AbstractRing for i64

impl AbstractRing for i128

impl AbstractRing for isize

impl<N: Num + Clone + ClosedNeg + AbstractRing> AbstractRing for Complex<N>

Implementors