Trait alga::general::AbstractSemigroup [−][src]
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, { ... } }
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: RelativeEq,
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,
Self: Eq,
Returns true if associativity holds for the given arguments.
Implementations on Foreign Types
impl AbstractSemigroup<Additive> for u8[src]
impl AbstractSemigroup<Additive> for u8fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for u16[src]
impl AbstractSemigroup<Additive> for u16fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for u32[src]
impl AbstractSemigroup<Additive> for u32fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for u64[src]
impl AbstractSemigroup<Additive> for u64fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for usize[src]
impl AbstractSemigroup<Additive> for usizefn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for u8[src]
impl AbstractSemigroup<Multiplicative> for u8fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for u16[src]
impl AbstractSemigroup<Multiplicative> for u16fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for u32[src]
impl AbstractSemigroup<Multiplicative> for u32fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for u64[src]
impl AbstractSemigroup<Multiplicative> for u64fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for usize[src]
impl AbstractSemigroup<Multiplicative> for usizefn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl<N> AbstractSemigroup<Multiplicative> for Complex<N> where
N: Num + Clone + ClosedNeg, [src]
impl<N> AbstractSemigroup<Multiplicative> for Complex<N> where
N: Num + Clone + ClosedNeg, fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl<N> AbstractSemigroup<Additive> for Complex<N> where
N: AbstractGroupAbelian<Additive>, [src]
impl<N> AbstractSemigroup<Additive> for Complex<N> where
N: AbstractGroupAbelian<Additive>, fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for i8[src]
impl AbstractSemigroup<Additive> for i8fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for i16[src]
impl AbstractSemigroup<Additive> for i16fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for i32[src]
impl AbstractSemigroup<Additive> for i32fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for i64[src]
impl AbstractSemigroup<Additive> for i64fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for isize[src]
impl AbstractSemigroup<Additive> for isizefn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for i8[src]
impl AbstractSemigroup<Multiplicative> for i8fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for i16[src]
impl AbstractSemigroup<Multiplicative> for i16fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for i32[src]
impl AbstractSemigroup<Multiplicative> for i32fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for i64[src]
impl AbstractSemigroup<Multiplicative> for i64fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for isize[src]
impl AbstractSemigroup<Multiplicative> for isizefn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for f32[src]
impl AbstractSemigroup<Additive> for f32fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Additive> for f64[src]
impl AbstractSemigroup<Additive> for f64fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for f32[src]
impl AbstractSemigroup<Multiplicative> for f32fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq, impl AbstractSemigroup<Multiplicative> for f64[src]
impl AbstractSemigroup<Multiplicative> for f64fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq, [src]
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, [src]
fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq,