Trait alga::general::AbstractRing

pub trait AbstractRing<A: Operator = Additive, M: Operator = Multiplicative>: AbstractGroupAbelian<A> + AbstractMonoid<M> {
    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.

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Implementations on Foreign Types

impl AbstractRing<Additive, Multiplicative> for i8

impl AbstractRing<Additive, Multiplicative> for i16

impl AbstractRing<Additive, Multiplicative> for i32

impl AbstractRing<Additive, Multiplicative> for i64

impl AbstractRing<Additive, Multiplicative> for isize

impl AbstractRing<Additive, Multiplicative> for f32

impl AbstractRing<Additive, Multiplicative> for f64

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

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Implementors

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