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: ApproxEq,
    { ... }
    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:

• A abstract operator (usually the addition) that fulfills the constraints of an abelian group.
• A second abstract operator (usually the multiplication) that fulfills the constraints of a monoid.

Provided Methods

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

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.

Implementations on Foreign Types

impl AbstractRing<Additive, Multiplicative> for i8

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

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

impl AbstractRing<Additive, Multiplicative> for i16

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

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

impl AbstractRing<Additive, Multiplicative> for i32

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

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

impl AbstractRing<Additive, Multiplicative> for i64

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

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

impl AbstractRing<Additive, Multiplicative> for isize

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

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

impl AbstractRing<Additive, Multiplicative> for f32

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

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

impl AbstractRing<Additive, Multiplicative> for f64

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

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

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

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

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

Implementors