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

pub trait AbstractSemigroup<O: Operator>: PartialEq + AbstractMagma<O> {
    fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool
    where
        Self: RelativeEq,
    { ... }

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

A semigroup is a quasigroup that is associative.

A semigroup is a set equipped with a closed associative binary operation and that has the divisibility property.

Associativity

∀ a, b, c ∈ Self, (a ∘ b) ∘ c = a ∘ (b ∘ c)

Provided methods

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

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

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

Returns true if associativity holds for the given arguments.

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Implementations on Foreign Types

impl AbstractSemigroup<Additive> for u8[src]

impl AbstractSemigroup<Additive> for u16[src]

impl AbstractSemigroup<Additive> for u32[src]

impl AbstractSemigroup<Additive> for u64[src]

impl AbstractSemigroup<Additive> for usize[src]

impl AbstractSemigroup<Multiplicative> for u8[src]

impl AbstractSemigroup<Multiplicative> for u16[src]

impl AbstractSemigroup<Multiplicative> for u32[src]

impl AbstractSemigroup<Multiplicative> for u64[src]

impl AbstractSemigroup<Multiplicative> for usize[src]

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

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

impl AbstractSemigroup<Additive> for i8[src]

impl AbstractSemigroup<Additive> for i16[src]

impl AbstractSemigroup<Additive> for i32[src]

impl AbstractSemigroup<Additive> for i64[src]

impl AbstractSemigroup<Additive> for isize[src]

impl AbstractSemigroup<Multiplicative> for i8[src]

impl AbstractSemigroup<Multiplicative> for i16[src]

impl AbstractSemigroup<Multiplicative> for i32[src]

impl AbstractSemigroup<Multiplicative> for i64[src]

impl AbstractSemigroup<Multiplicative> for isize[src]

impl AbstractSemigroup<Additive> for f32[src]

impl AbstractSemigroup<Additive> for f64[src]

impl AbstractSemigroup<Multiplicative> for f32[src]

impl AbstractSemigroup<Multiplicative> for f64[src]

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Implementors

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

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