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

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, 

impl AbstractMonoid<Additive> for u16

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, 

impl AbstractMonoid<Additive> for u32

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, 

impl AbstractMonoid<Additive> for u64

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, 

impl AbstractMonoid<Additive> for usize

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, 

impl AbstractMonoid<Multiplicative> for u8

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, 

impl AbstractMonoid<Multiplicative> for u16

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, 

impl AbstractMonoid<Multiplicative> for u32

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, 

impl AbstractMonoid<Multiplicative> for u64

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, 

impl AbstractMonoid<Multiplicative> for usize

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, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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: RelativeEq, 

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

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Implementors

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

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