[][src]Trait alga::general::AbstractMonoid

pub trait AbstractMonoid<O: Operator>: AbstractSemigroup<O> + Identity<O> {
    fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool
    where
        Self: RelativeEq
, { ... }
fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool
    where
        Self: Eq
, { ... } }

A semigroup equipped with an identity element.

∃ e ∈ Self, ∀ a ∈ Self, e ∘ a = a ∘ e = a

Provided Methods

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

Checks whether operating with the identity element is a no-op for the given argument.

Implementations on Foreign Types

impl AbstractMonoid<Additive> for u8
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impl AbstractMonoid<Additive> for u16
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impl AbstractMonoid<Additive> for u32
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impl AbstractMonoid<Additive> for u64
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impl AbstractMonoid<Additive> for usize
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impl AbstractMonoid<Multiplicative> for u8
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impl AbstractMonoid<Multiplicative> for u16
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impl AbstractMonoid<Multiplicative> for u32
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impl AbstractMonoid<Multiplicative> for u64
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impl AbstractMonoid<Multiplicative> for usize
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impl<N> AbstractMonoid<Multiplicative> for Complex<N> where
    N: Num + Clone + ClosedNeg
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impl<N> AbstractMonoid<Additive> for Complex<N> where
    N: AbstractGroupAbelian<Additive>, 
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impl AbstractMonoid<Additive> for i8
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impl AbstractMonoid<Additive> for i16
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impl AbstractMonoid<Additive> for i32
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impl AbstractMonoid<Additive> for i64
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impl AbstractMonoid<Additive> for isize
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impl AbstractMonoid<Multiplicative> for i8
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impl AbstractMonoid<Multiplicative> for i16
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impl AbstractMonoid<Multiplicative> for i32
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impl AbstractMonoid<Multiplicative> for i64
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impl AbstractMonoid<Multiplicative> for isize
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impl AbstractMonoid<Additive> for f32
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impl AbstractMonoid<Additive> for f64
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impl AbstractMonoid<Multiplicative> for f32
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impl AbstractMonoid<Multiplicative> for f64
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Implementors

impl<O: Operator> AbstractMonoid<O> for Id<O>
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