[−][src]Trait alga::general::AbstractGroupAbelian

pub trait AbstractGroupAbelian<O: Operator>: AbstractGroup<O> {
    fn prop_is_commutative_approx(args: (Self, Self)) -> bool
    where
        Self: RelativeEq,
    { ... }

    fn prop_is_commutative(args: (Self, Self)) -> bool
    where
        Self: Eq,
    { ... }
}

An Abelian group is a commutative group.

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

Commutativity

∀ a, b ∈ Self, a ∘ b = b ∘ a

Provided methods

fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq, 

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications.

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

Returns true if the operator is commutative for the given argument tuple.

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Implementations on Foreign Types

impl<N> AbstractGroupAbelian<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg, [src]

impl<N> AbstractGroupAbelian<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, [src]

impl AbstractGroupAbelian<Additive> for i8[src]

impl AbstractGroupAbelian<Additive> for i16[src]

impl AbstractGroupAbelian<Additive> for i32[src]

impl AbstractGroupAbelian<Additive> for i64[src]

impl AbstractGroupAbelian<Additive> for isize[src]

impl AbstractGroupAbelian<Additive> for f32[src]

impl AbstractGroupAbelian<Additive> for f64[src]

impl AbstractGroupAbelian<Multiplicative> for f32[src]

impl AbstractGroupAbelian<Multiplicative> for f64[src]

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Implementors

impl<O: Operator> AbstractGroupAbelian<O> for Id<O>[src]

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