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: ApproxEq,
    { ... }
    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

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

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.

Implementations on Foreign Types

impl AbstractMonoid<Additive> for u8

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

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

impl AbstractMonoid<Additive> for u16

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

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

impl AbstractMonoid<Additive> for u32

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

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

impl AbstractMonoid<Additive> for u64

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

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

impl AbstractMonoid<Additive> for usize

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

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

impl AbstractMonoid<Multiplicative> for u8

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

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

impl AbstractMonoid<Multiplicative> for u16

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

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

impl AbstractMonoid<Multiplicative> for u32

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

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

impl AbstractMonoid<Multiplicative> for u64

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

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

impl AbstractMonoid<Multiplicative> for usize

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

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

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

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

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

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

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

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

impl AbstractMonoid<Additive> for i8

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

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

impl AbstractMonoid<Additive> for i16

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

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

impl AbstractMonoid<Additive> for i32

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

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

impl AbstractMonoid<Additive> for i64

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

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

impl AbstractMonoid<Additive> for isize

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

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

impl AbstractMonoid<Multiplicative> for i8

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

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

impl AbstractMonoid<Multiplicative> for i16

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

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

impl AbstractMonoid<Multiplicative> for i32

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

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

impl AbstractMonoid<Multiplicative> for i64

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

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

impl AbstractMonoid<Multiplicative> for isize

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

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

impl AbstractMonoid<Additive> for f32

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

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

impl AbstractMonoid<Additive> for f64

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

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

impl AbstractMonoid<Multiplicative> for f32

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

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

impl AbstractMonoid<Multiplicative> for f64

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

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

Implementors

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