# [−][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 monoid is a semigroup equipped with an identity element, e.

A set equipped with a closed associative binary operation with the divisibility property and an identity element.

# Identity element

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

## Provided methods

### `fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
Self: RelativeEq,`

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

### `fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
Self: Eq,`

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

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## Implementations on Foreign Types

### `impl AbstractMonoid<Additive> for u8`[src]

### `impl AbstractMonoid<Additive> for u16`[src]

### `impl AbstractMonoid<Additive> for u32`[src]

### `impl AbstractMonoid<Additive> for u64`[src]

### `impl AbstractMonoid<Additive> for usize`[src]

### `impl AbstractMonoid<Multiplicative> for u8`[src]

### `impl AbstractMonoid<Multiplicative> for u16`[src]

### `impl AbstractMonoid<Multiplicative> for u32`[src]

### `impl AbstractMonoid<Multiplicative> for u64`[src]

### `impl AbstractMonoid<Multiplicative> for usize`[src]

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

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

### `impl AbstractMonoid<Additive> for i8`[src]

### `impl AbstractMonoid<Additive> for i16`[src]

### `impl AbstractMonoid<Additive> for i32`[src]

### `impl AbstractMonoid<Additive> for i64`[src]

### `impl AbstractMonoid<Additive> for isize`[src]

### `impl AbstractMonoid<Multiplicative> for i8`[src]

### `impl AbstractMonoid<Multiplicative> for i16`[src]

### `impl AbstractMonoid<Multiplicative> for i32`[src]

### `impl AbstractMonoid<Multiplicative> for i64`[src]

### `impl AbstractMonoid<Multiplicative> for isize`[src]

### `impl AbstractMonoid<Additive> for f32`[src]

### `impl AbstractMonoid<Additive> for f64`[src]

### `impl AbstractMonoid<Multiplicative> for f32`[src]

### `impl AbstractMonoid<Multiplicative> for f64`[src]

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## Implementors

### `impl<O: Operator> AbstractMonoid<O> for Id<O>`[src]

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