# [−][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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