Trait alga::general::AbstractSemigroup

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

An associative magma.

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

Provided Methods

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

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.

Implementations on Foreign Types

impl AbstractSemigroup<Additive> for u8

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

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

impl AbstractSemigroup<Additive> for u16

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

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

impl AbstractSemigroup<Additive> for u32

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

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

impl AbstractSemigroup<Additive> for u64

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

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

impl AbstractSemigroup<Additive> for usize

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

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

impl AbstractSemigroup<Multiplicative> for u8

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

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

impl AbstractSemigroup<Multiplicative> for u16

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

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

impl AbstractSemigroup<Multiplicative> for u32

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

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

impl AbstractSemigroup<Multiplicative> for u64

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

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

impl AbstractSemigroup<Multiplicative> for usize

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

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

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

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

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

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

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

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

impl AbstractSemigroup<Additive> for i8

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

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

impl AbstractSemigroup<Additive> for i16

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

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

impl AbstractSemigroup<Additive> for i32

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

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

impl AbstractSemigroup<Additive> for i64

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

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

impl AbstractSemigroup<Additive> for isize

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

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

impl AbstractSemigroup<Multiplicative> for i8

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

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

impl AbstractSemigroup<Multiplicative> for i16

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

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

impl AbstractSemigroup<Multiplicative> for i32

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

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

impl AbstractSemigroup<Multiplicative> for i64

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

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

impl AbstractSemigroup<Multiplicative> for isize

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

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

impl AbstractSemigroup<Additive> for f32

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

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

impl AbstractSemigroup<Additive> for f64

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

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

impl AbstractSemigroup<Multiplicative> for f32

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

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

impl AbstractSemigroup<Multiplicative> for f64

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

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

Implementors

• impl<O: Operator> AbstractSemigroup<O> for Id<O>